Battle of the Fords of Isen

But for the sake of argument, lets say this operation actually takes place. How would this happen?
In the book, there were two battles at the Fords of Isen. The first saw Theodred advance across the river and march north with 8 companies. Three were left on the other side. The goal was to destroy Saruman's army before it was able to gather and advance into Rohan. But Saruman knew the attack was coming. So he had already deployed his army into entrenched positions. The Uruk-hai were waiting with orders to kill Theodred at all costs. Rohan's forces were forced to retreat. A smaller force with warg riders was able to cross the river and attack the unprepared forces on the Eastern side, defeating them.
Theodred was essentially left trapped on an small island in the middle of the Fords. Instead of pursuing the rest of the retreating forces, Isengard's forces turned and unleashed their full power on Theodred. Some of the Rohirrim were able to get to him just after he was killed. A second group of 4 companies arrived and routed the Uruk-hai.
A couple of interesting things jump out at me for the First Battle. First, Saruman's skill at deception allowed him to secure initial tactical successes. Second, it demonstrated that Saruman did in fact learn how to effectively defeat mounted troops. His use of trenches and pike formations demonstrates that he was able to exploit both of these. Add in the artillery batteries I suspect Isengard would actually have and this would have been much more powerful.
The next shows Rohan's skills. Yes, Rohan was forced to retreat. But the pursuing enemy was cut down several times. Like what one would expect from a culture quite skilled at mounted tactics. The feigned retreat and Parthian Shot both allow for powerful fighting retreats. Then, a lot of Isengard's losses came from traditional mounted charges under conditions favorable to Rohan. For example, Theodred's relief came from the rearguard units. The attacking uruks were hit from behind and caught between hammer and anvil essentially.
This priority on killing Theodred would prove essential for Rohan's eventual victory though. There was a point where a breakthrough had been achieved and a quick strike on Edoras could have been accomplished. This would have cut off reinforcements from the city reaching Helm's Deep. Gandalf would have been intercepted too. Essentially, Theodred's death would prove to be a tactical victory for Isengard that made a strategic one much harder to achieve.
The second was the attempt at the main invasion. Rohan stationed forces on both sides. The memory of the first battle led Rohan to feel that the eastern side was where the main attack would come from. But by exploiting the speed of the wargs, Isengard was able to get forces between the two groups of Rohirrim in the battle. One was surrounded and the other was almost encircled. The first group was forced to retreat to the eastern side after taking heavy losses. It formed a shield wall around the camp and fought on.
The other conducted a full retreat. The commander of the encircled force knew help was not coming and that he could not last forever. So he attempted to break out. Two separate groups charged the uruks. This was successful, partially due to Rohan exploiting the cover of darkness. The Uruks were successfully confused enough to allow even Rohan's foot soldiers to escape.
The second battle was much more strategically useful. Yes, no high level commander was killed. But it allowed Isengard to secure the area. Supply lines were established. Saruman could then move his troops to Edoras, Dunharrow and Helm's Deep.

The Conflict

Prelude

After the discovery of his deceptions, Saruman's hand would be forced. He would send out his army to invade Rohan as soon as possible. But this same discovery of his treachery would also mean that Rohan would expect this attack. This would mean a couple of things. First, the evacuation of the capital. Retreating to Helm's Deep was a wise move by Theoden.
But also important is the fact that Helm's Deep was the responsibility of the Second Marshal of the Riddermark - Théodred. Which means he would most likely not be sent to fight at the Fords of Isen. The Third Marshal, Eomer, would have to fill in. This is an important shift. Isendard's tactics in the books were based on killing Théodred. Without such a high value target there, more conventional tactics would be used.
Eomer is a highly important person, but he was also not the son of the king. Which means that his death does less to eliminate the government of Rohan. It is true that he would be a huge loss to Rohan, but more in the operational sense. Theodred is the one whose death would further Saruman's strategic ambitions. So the uruks would naturally seek to kill Eomer, but probably not have the same orders to kill at all costs.

Deployment

Should Isengard invade, his plan would likely be a grander version of both rolled into one battle. Remember, his goal is to do as much damage as possible as quickly as possible. Which means that he needs to kill, capture or rout as many of the Rohirrim as possible. If he could wipe out the entire Rohirrim here, he would. So long as he gets uncontested control over the river though, he would be in a solid position.
He would set up prepared positions and bait the Rohirrim into attacking him. But here is where things get interesting. Saruman would need as much speed as possible after the battle. Yet his artillery would be the best asset available to defeat Rohan. So these prepared positions would probably be artillery batteries made up of the big guns. The smaller guns, which are normally designed to keep up with the advancing army, would be kept in reserve.
These would probably be strung out along the river so that they could all fire at the crossing point. These would probably be mainly supplied mortar shrapnel rounds the further down the line the guns get. The idea is to have the focus be on hitting the front ranks of the enemy to force them into retreat through sheer firepower. The others would then be set up to rain down on the rest of the force, ideally hitting the rear areas too.
These would probably have individual protection. The most important would be camouflage so the artillery fire would come as a surprise as long as possible. Then, there would need some sort of earthwork idea to keep explosions in one battery from damaging neighbors. Then, each would greatly benefit from archers or crossbowmen to protect against attackers.
The rear areas would be covered with trenches with at least two ranks of pike men. Trenches would be quite easy to build and provide a solid source for the earthwork barriers. They would then allow for a continuous barriers to attack from the rear. This maximizes the defensive power of pikes, which suffer if there are gaps or low density of points facing the enemy. This would also be a powerful compliment to the archers in each battery. The end result is that charges would most likely fail. By some miracle, should the Rohirrim get across the river, they would still have to face the entrenched positions calculated to stop them.
The second part of the plan would be the use of the Dunlendings and Warg Riders. Probably scout formations similar to what he attacked the Fellowship with would be part of this force too. They would wait in the hidden areas of the Dunlendings to attack when the Rohirrim are fully engaged.
As for the forces involved, I would suspect that the entire force would be sent out. Meaning 25,000 total men. The majority would be held on the western side waiting to break through. The other side would have decent amount of forces too though. I would estimate that the bulk of the Wild Men and warg riders would be sent to the other side in advance. Meaning 1,000 to 2,000 Dunlendings and 1,000 to 1500 warg-riders. The uruks sent over would probably be close to 2,000. This is based on the more limited estimates of Isengard's forces in the canon battles and the fact a larger force would probably be too big to cross over.
Rohan's deployment would probably be similar to the books. The original force sent to the first battle was 1,320 men in 11 eored. An additional 4 (with 480) arrived after diverting their path from Helm's Deep. The rest would still be mobilizing.

Battlefield

So, the Fords of Isen were the only place one could cross the River Isen into Rohan. Technically, Isengard was able to send a few troops over the water close to the source. But this was likely not good enough for the full army. Basically, if one wishes to invade from the west, this is the place to do it. Crossing rivers tends to give the advantage to the defenders. So the better tactician would be the one that can stay on their own side and bait the other into attacking.
An important element of the Fords is the tiny island in the middle. This proved a useful place to defend, especially in the first battle in the books. So if one wishes to defend against an invasion, swift seizure of this island would be a high priority. So much so that it appears one could effectively replicate the basics of Thermopolae. A small number of infantry could theoretically hold off a much larger force through defending a bottleneck.

The Engagement

Now the fun begins. Once everything is in place, Saruman would leak to Rohan that Isengard's forces on the move. Obviously he would disguise the source of the information and leave out the key details of them already being in entrenched positions. Eomer, recognizing the importance of the Fords of Isen, would send his forces to take and hold the Fords. Ideally, this would involve rushing mounted infantry to the island in the middle to hold the crossing. His forces would then aim to move across to meet the uruks while they are on the move.
That is a pretty solid plan for Rohan if reality met expectations. But we know that Saruman essentially prepared to turn such a plan into a bloodbath. The initial attacks would essentially get surprised by the entrenched positions. The result would be massive losses and a bit of a chaotic press as the men in the rear continue to press forward as the front is trapped. Once this happens, the scout, Wild Men and warg riders would attack from behind and the cannons would begin to fire. Things would not go well. We can expect that once this happens, there would be no hope for Rohan achieving even a tactical victory.
The original Rohirrim force would be ground down after being surrounded and trapped in the river. The attacks on all sides would be hard for anyone to break out of. But the combination of surprise from the flanking force and the totally unexpected shock of facing cannons for the first time would be brutal both mentally and in terms of numbers. A Uruk phalanx would begin to march across the river to deliver the killing blow.
But one key factor here is the force heading to Helm's Deep. In the books, they noticed Isengard's troops sent over to the eastern side before they were able to engage. Which is why 4 companies were sent that ended up saving the day. It seems unlikely that they would also not notice in this version. Which means it would be Rohan's turn to surprise their enemies. They would end up attacking the Wild Men and Wargs from the back, this time doing a lot of damage. Surprise, rear attacks on unprepared units not geared to defending against mounted charges would likely see this force take significant losses.
But it would also be clear that the best that can be hoped for is the trapped pocket of Rohirrm will escape. No one at this point would actually expect any sort of victory for Rohan. Instead, once the opportunity to escape is presented, it will be taken with the utmost haste. Most likely, it will be effectively a total rout. The wargs and Wild Men would pursue for as long as possible, inflicting even more losses.

Outcome

The main outcome would be the inevitable attacks on Edoras, Helm's Deep and Dunharrow. Saruman would know the value of all these places and would send some forces to all of them. But he would know that Edoras would be functionally deserted by the retreat to Helm's Deep. Dunharrow serves as a vital rally point for Rohan and losing it would cost Rohan an important base for future guerrilla actions. But it would also have minimal defenses.
Meanwhile, Helm's Deep is a hugely important target. Rohan's remaining currently mobilized forces and political leadership would be here. Then there is the huge benefits that the Glittering Caves and the Deeping Wall would confer on Isengard. So the main force of Isengard would be sent to Helm's Deep. Small detachments would be sent to take or at least destroy important infrastructure at Edoras and Dunharrow.
Meanwhile, the survivors of the Fords of Isen would eventually reform. The slow mobilization of troops would mean a trickle of reinforcements to this group. They would probably begin their campaign of hit and run attacks. This would continue until the force gets to Helm's Deep. Which would in part provide useful reinforcements needed for the defense. Plus, the news of cannons would be useful information for the defenders too. But the impact of shattered troops might be a morale drain on the garrison. The extent of this will depend on what proportion of these reinforcements were at the Fords of Isen and how many successful raids on the attackers they were able to pull off during the retreat.