Reunification of Gondor and Rohan

Gondor's expansion doesn't just encompass its former enemies. It also peacefully reclaims former lands intentionally given up. Which poses special challenges and opportunities. On one hand, it does not need to apply force to secure rule over Rohan. But it also can't use force. So if things turn bad, the problems have a shorter list of wise options than in other areas.

The Conflict

Deployment

Now - there is one major issue that needs to be addressed. The genocide against the Wild Men. It seems highly unlikely that this would not be taking place. As noted elsewhere, Theoden would need to do something to regain the trust of his people and eliminate rivals in order to retain his power. Riding the popular hatreds of the people to their most extreme ends would allow him to do both. But there is a severe problem with this militarily - the Ents and the Elves.
Genocide does harm that is lasting, certain and grave. Stopping Rohirrim attacks does not require genocide against Rohan, so intervention would not be as harmful as what it intends to stop. Theoden would probably not have the time or inclination to negotiate. The nature of the Entmoot also means any intervention would have popular support and come from a legitimate authority. Intervention can prevent evil acts and potentially be carried so far as to punish the government should it fail to restrain itself.
Meanwhile, refusal to intervene would be peacefulness in the face of evil only preventable through force. There is no moral issue in St. Augustine's works for using violence to protect peace or punish evil. Stopping genocide would count as both. All this to say that there is no doubt that the Ents would intervene to protect the Wild Men. It clearly fits with the interpretation of Just War Theory that I applied to the Ents.
Then we have the Elven "Clinton Doctrine". Genocide tends to be quite destabilizing, causes a large refugee flow and is a clear humanitarian crisis. And "genocide is a human rights violation" is one of the most obvious statements ever. Human rights violations are one of the cases justified on humanitarian grounds by the Clinton Doctrine. So yeah, the elves would be deploying forces here to stop Rohan from wiping out the Wild Men.

Battlefield

So many different conflicts would be emerging that would require Rohan's territory to solve. The first is the one on its land directly - the genocide against the Wild Men. Without permission to move in, Gondor or elven interventions to stop it could be seen as an act of war. Secondly, Arnor is also Gondor's territory. Due to White Easterling and Wild Men refugees, ethnic conflicts would be rising there too. We will get to that later though. Rohan would be the quickest way to get to this area. Lastly, Saruman would be resurgent in the Shire - also Gondor's territory. If Gondor is unable to pass through Rohan, securing the Shire would become a problem.

Conditions

Now, Rohan's economy clearly does not have what is needed to rebuild Gondor and get its finances in line. But, it does have the Glittering Caves. Which is apparently quite rich in mineral resources. We also know that Moria has influence over Rohan that Moria would try to exploit to get those resources. Gondor would have been reunited with Rohan. It too is in a position that makes it vulnerable to Dwarven economic manipulation. The Lonely Mountain is already not happy with Gondor and is likely to be distracted with the Easterling Civil War.

The Engagement

So, how would Aragorn secure an alliance with Rohan past the Battle of Minas Tirith? First I would capitalize on the marriage of Faramir and Eowyn by promoting Faramir to the top military position in Gondor and giving Eowyn a top level civilian position. I would give Eomer promises to help defeat the wild men that aided Saruman during the war with Isengard. Then I would send some of the aid I get to Rohan to help with their rebuilding.
This would have several important political implications. Most obviously it would incorporate the political elites of Rohan into Gondor's establishment. Which then lessens the threat of revolt. Granted, it seems unlikely that Rohan would. But there would be some who would value Rohan's independence and fear the loss of local control. So retaining and incorporating the established elites into Gondor's establishment, these fears would be mitigated. At the same time, Rohan's elites would not have a stake in the continuation of Gondor's regime as they are part of it now.
From Gondor's perspective, two important benefits would be gained. First is the Rohirrim. More soldiers would be a huge help in a time of crisis. But thankfully the post Minas Tirith period should start to see a decline in the need for soldiers actively fighting. What would be more important is the food. Remember that Rohan's main economic activity would be meat and dairy production. By incorporating Rohan into Gondor, Aragorn would remove one barrier to getting that food into Gondor. Which could then could prevent famine.
Now, Aragorn would need to do something to retain the loyalty of Rohan. This is where the impacts of Saruman's attacks would come in. Remember the escalation of tensions with the Wild Men leading to genocide? Well, this is where this story ends. Because I am not trying to change things without reason, Theoden still dies and Eomer takes the throne of of Rohan. Eomer was not compromised by the subversion of Saruman, so there is nothing politically to gain from allowing the massacres of Wild Men to continue. Aragorn and Eomer both have a lot to gain actually from bringing peace to the area. Neither benefit now from seeing Rohan rip itself to shreds on ethnic lines.
So Aragorn would lend some troops to Eomer. Eomer would then take these men into Rohan to clamp down on the genocide. Once order has been imposed, it would be clear that the new order is in charge. The Wild Men are likely to mostly be gone. Whether this is from murders, fleeing into Arnor or following Saruman into the Shire, it matters little. But the Wild Men would not feel threatened as much as the areas they now live in are controlled by the people who stopped the murders. They might not feel safe, but not actively hunted either. Which would be a vast improvement.
Once Gondor moves in to stop this, the elves would back off. The Nixon Doctrine posits that a government's local forces would need to carry the main burden and leadership. Now that there is a local partner to fill the role of genocide prevention, this provision kicks in. The Elves would probably lend support to Gondor in its efforts. But the elven forces would no longer be taking the primary or possibly even an active role.
Just as important is the fact that new elites would be in charge now. The top man pushing for the genocide is dead. The new leader of Rohan is more moderate. Gondor would be stepping in to administer the region and thus would prove a stabilizing influence. Basically, negotiations are now possible and much more likely to work. Which then means that Just War Theory demands hostilities cease and talks begin. Which means that the Ents would begin to draw down their intervention too.
But there is likely to be a decent amount of fighting. These forces would provide a stabilizing influence through their mere presence. But enough will be killed to drive Wild Men from the area. Some Elves and possibly Ents might be killed. Certainly some Rohirrim. But it would end. And would probably not wipe out all the Wild Men as a result. But it will likely be enough to be genocidal.
This then opens up the possibility of men being sent to the Shire. A final defeat of Saruman would grant Eomer a political victory that would help secure his power. Basically, Eomer would want to paint himself as the driving force behind finishing off Rohan's main foe. Then, the incorporation into Gondor would be seen as a key tool in doing so. Similar to how Aragorn's ascension was vital to Gondor getting needed elven aid.
Most importantly to me would be nobles from Rohan. Remember prior to this Rohan had a very long history of independence, a distinct culture and established political elite. By granting them land conquered by Gondor by the king of Gondor on the condition they improve Gondor’s security, it could be a very effective way to begin blending the two states. Then, respecting their autonomy would be important too. By allowing the established elites in Rohan retain as much political control as possible would go a long way towards ensuring loyalty.
Now, economically, the Glittering Caves would be the most obvious main resource to exploit. Which means that mining concessions to the Glittering Caves would be a solid option. Importantly, it gets the technical expertise and manpower in to do it. Then, the royalties agreed to would go a long way towards helping Gondor recover. And even if it doesn't completely cover it, it makes Moria happy. So Moria itself would become more likely to fill Gondor's deficit. One of the tools governments can use to resolve financial issues with is this same sort of move. This, most importantly for us, would generate a high amount of revenue for the state.
But just as important is the fact it relies on a small number of outside players. This reduces their domestic power base, making them more dependent on the grantor of the concessions. The smaller the group allows them to be better monitored and controlled. Just as important politically is the rewards for loyalty. The best way to buy loyalty of a group is huge amounts of private goods - salaries, bribes, fancy estates and so forth. This becomes prohibitively expensive if the group gets too big. But mineral concessions to elite outsiders is an ideal way to keep the group in question small.
So securing the Glittering Caves for Gimli would be hard. First, there is the issue of location. How does one exploit the mineral reserves of the Glittering Caves without compromising Helm's Deep's defensive power? That is more of an engineering problem than I am able to solve. So I'll ignore that for now. The much bigger issue is granting this concession would inflame the passions of Rohan. Helm's Deep is such an important site that I doubt they would take kindly to its commercial exploitation by dwarves.
The other question is who gets to rule the Glittering caves. Gloin, Gimli’s father, was still alive, so he might try and secure the throne for himself due to his claim being the only one more legitimate than Gimli. But Aragorn needs Gimli due to their personal connections. So, the question becomes how to get Gimli on the throne over his own dad.
The first option would come down to faster army diplomacy. If I were Aragorn, I would first get some of my men to “escort” Gimli back to the Glittering Caves with the hope of getting him there before any challengers could. Lets say 50 Tower Guards and 8 Rangers. This group would have secret orders to kill Gloin should he show up. I would outfit the subgroup (8 rangers) tasked with this order with orc equipment scavenged from the battlefield and concealed during the journey. The idea is to make it look like the orcs did it. Now, ideally it would not come to that. Gloin giving in or preferring to stay at the Lonely Mountain, getting killed on the way or agreeing to the deal offered Gimli would all work just as well if not better. Given we have no real information on what Gloin did after the Hobbit, it is hard to tell what he would do. Thus, an insurance policy would be in order.
I mentioned a deal offered to Gimli. What would that be? Well, obviously Moria would send the money needed to keep the Gondor government afloat and finance the rest of the war and reconstruction efforts. This would mean not just sending money, but raw materials as well. Mithril, iron and copper are both really useful to make weaponry out of and require a use to have economic value. Unlike gold and silver, they are not used as currencies or seen as wealth in their own right. Meanwhile, Moria obviously lacks farming potential, seeing as it is completely inside a mountain. Gondor’s main thing is agricultural products, so it could offer Moria food products.
Also, like real-world aid, some of the aid could be provided on the condition that it be used to purchase stone, iron, copper, mithril and possibly manufactured for the reconstruction efforts and and for new weaponry needed to continue the war effort. These would probably be provided at inflated costs and the food at below market value while the remainder not repaid in goods would have interest attached to it. I would imagine this would play into both sides needs and strengths enough. I suspect that the friendship would mean that both sides would probably offer more concessions to the other than would be found in normal bilateral aid/trade agreements. Especially when one is as vulnerable as Gondor is at this point. But Gimli isn’t exactly in a strong place either. He is just dealing with a limited labor force, short time on the throne and harassment from orcs. Gondor is the one totally on the verge of economic collapse, militarily crushed even when victorious, ravaged economic base and large amounts of population loss – all with strong enemies still on the frontier and organized.

Outcome

Given the amount of reading I have done on the Russian Civil War, you would think that the Cossacks would be the obvious culture to look at when trying to build a society like Rohan. But it seems that I would be hard pressed at this point not to see Cossacks as a viable inspiration for this part of the narrative.
So, one thing that makes this situation tricky for Aragorn is the nature of the reunification itself. It was quite easy due to their long standing economic and political ties. But enforcing control would be much harder. In normal conquests, one can use force of arms to dislodge the local elites and replace them with the people one wants. Think the Norman Conquest for example. But this is not something that is the case here. So Gondor has to rely on the cooperation of already established elites.
These elites have their own culture and power base. They are also used to a high degree of autonomy, freedom of movement and low taxation. The central government was distrusted by the people. At best it was a figurehead representing the whole country. But in terms of actual authority, it appears to be resented. At best it was a burden to be tolerated in limited cases.
Then you have the Cossacks for comparison. They had a long history of independence, self rule and even democratic governance. Conflicts between expansionist and autocratic Russia seemed inevitable. Rebellions against harsh Russian bureaucracy were launched. So too were pro-independence and anti-slavery revolts. These led to brutal repression and destruction of Cossack independent control over their territory.
But they were eventually recognized as important parts of Russian society by the government. They were granted legal rights and privileges that made them similar to Roman Auxilia or medieval knights. They had to provide their own supplies and horses. But the Russian government provided them with firearms, ammunition and the related equipment. Their terms started out as 20 years. But this was reduced to 18 years - 5 active duty and the rest in reserves. Socially they were granted tax exempt status.
This system proved highly effective in securing political reliability. This reliability became one of their strongest assets in the eyes of the government. They then became essential parts of the Russian military in several important wars - including the Napoleonic Wars. Increasingly they became enforcers of the government. The image of the Cossack on their horse and using their distinctive whips to beat protesters was one of the symbols of the hated Tsarist police system.

Aftermath

But this system could not last. Especially after the Russo-Japanese War, there was a clear need for professionalization of the military. The Cossacks were not seen as well trained and disciplined as the traditional cavalry. Granted, they were seen as great in scouting and ambushes. Which meant that their traditionally strong formations were broken up into smaller ones for light cavalry roles. Or simply used as messengers or escorts meant to look pretty. Their traditional, semi feudal status was seen as obsolete and their initiative and rough riding skills became under appreciated.
Seaton, Albert (1972). The Cossacks. Random House. ISBN 978-0-85045-116-0.
Almost as important in the coming issues with the Cossacks was the eventual decline in the role of cavalry. This was especially true in World War One. With the advent of trench warfare and increasing popular resistance, the security role of the Cossacks became practically the only one they were used in. This included rounding up deserters and even stampeding protesters. Razing villages and farms during retreats also fell on them.
This not only turned people against the government but against the Cossacks. As this was happening, the Cossacks were seeing their list of grievances increasing. Granted, between 1905 and 1917, most of the demands were more liberal and reformist rather than radical. Once the February Revolution started though, there was a clear break. Most of the Cossacks in Petrograd defected to the demonstrators. Despite them being a small number of the garrison, their history and status made this defection a highly important act that helped signal the end of the Tsar.
We are a bit lucky when drawing on Cossack history here. Russia had a moderate and liberal, legislator driven revolt similar in some respects to the French. Both also were led by the urban middle and upper classes, professionals and merchants. There were a lot of major differences, but I feel the February Revolution and the French Revolutions were close enough to allow us to see what the "Cossack" Rohirrim would do. In this case, they would probably side with the revolution. Men would refuse to perform their traditional role as riot police and instead push for more local autonomy, preservation of privileges and keeping their units together.
But should the narrative take a turn in the October Revolution, then you get a whole other ball game. The Cossacks were much more divided and the Rohirrim would probably be too. The Cossacks were generally more aligned with the White forces. But many were sick of the fighting and refused to join either side. Lower class civilians and rank and file troops tended to have a higher percentage join the Bolsheviks. It was the officers and landowners that tended to naturally be the more militant White supporters. But it seems that the fear of losing what their legal status meant higher than normal levels of support for the Whites.
But Aragorn did take some liberalizing actions before the October revolution. He also would be the natural leader of the "whites" in Gondor. So he would become the focal point for the local opposition to the revolutionary government. Rohan though has several advantages that the Cossacks did not have in the Russian Civil War. The first is the distance between Rohan and Minas Tirith is a lot less than the Kuban Host and Petrograd. There would be no significant minority presence in the area also seeking autonomy. The legacy of genocide would leave no openings for a divide and conquer option.