Hammerfell left the Empire and drove out the Aldmeri Dominion. Why do you seem to think such a thing is impossible for Skyrim to accomplish as well?
First of all, Hammerfell DID NOT "drive out" the Thalmor. They fought them to a stalemate and eventually negotiated an end to open hostilities. With that in mind, do you think the Thalmor threw everything they had into the invasion of Hammerfell? Yes or no? If yes, why would such a move make any kind of sense? Remember that if everything they have is tied up in Hammerfell then NOTHING is preventing the Legion from marching along the coast, preventing a retreat, and then falling into the back of the Thalmor.
If no, would you not agree that if what they did invest was enough for a stalemate then "everything they have" would probably have achieved more?
Why do you think Skyrim absolutely has to be part of the Empire, no matter what?
Without Skyrim, the Empire is almost certain to fall and once the Empire falls, the Thalmor lose the big adversary that ties up many of their troops. Then they can focus 100% on taking out the rest of the lands of man. The issue isn't what happens next year or next decade but what will almost certainly happen within the next few centuries. That's the time scale the Thalmor operate on.
It doesn't matter what Ulfric wants. Even if he is the face and head of the rebellion, his actions or beliefs do not condemn every Nord in Skyrim fighting for independence.
What does condemn every Nord in Skyrim fighting for "indepdence" is the fact that they're playing into the Thalmor game of divide and conquer. Skyrim won't be stronger for not being allied with Cyrodiil and High Rock and the Empire won't be stronger for being reduced to two provinces that don't share a land border. In fact both the Empire and Skyrim will be weakened while nothing negative has happened to the Thalmor. When their strength remain unchanged while their enemies grow weaker, they are effectively strengthened.
In other words, Ulfric is fighting the wrong enemy and his doing so is of immense benefit to the real enemy. It is, in my opinion, the duty of every free Tamrielic citizen of good conscience to fight evil and oppression as best they can, and currently evil and oppression is strongly represented by the Thalmor. You don't fight the Thalmor by making them stronger relative to their enemies, you fight them by subverting their plots and killing their agents, whenever you can. They want a civil war so the anti-Thalmor thing to do is to not give them one. They want division between the lands of men so the anti-Thalmor thing to do is to stand more united than ever.
They can't win unless they can divide men to fight against men. They. Can't. Win. So the anti-Thalmor thing is to do what will certainly deny them victory and NOT START WARS BETWEEN THE LANDS OF MEN. It really is that simple. In his failing to understand this, Ulfric has led countless strong Nords astray, who are in turn fighting the Thalmor's battle for them. His treachery against all that is righteous is quite impressive, and the only thing that speaks in his defense is that he doesn't do all this knowingly. Even so, he's simply a pawn. If Torygg was an Imperial puppet then the same can definitely be said about Ulfric's relationship with the Thalmor. Sure, he hates them and doesn't willingly aid them, but he's being played and used all the same.
The Aldmeri Dominion would have defeated the Empire, not everyone.
Without the Empire to stand in their way, who exactly do you see emerging victorious in time? Do you think Hammerfell could suddenly go on the offensive and invade Summerset Isle, when the Empire of old could not? It's not about sudden and quick conquests. That's not how the Thalmor operate anyway. It's about very slow and very well hidden power plays that take place over so many years that most people don't notice it. Once the Thalmor control Cyrodiil, they have a huge land area in mainland Tamriel as well as a totally safe home base on Summerset Isle. Look on a map and see just how vulnerable this would leave Hammerfell. Not within the first few years of Cyrodiil falling, of course. That would be hasty. The Thalmor would take their time and completely break Cyrodiil first, and only then, when uprisings are impossible because of decimation after decimation, they'd start going offensive.
It would take decades or even centuries, but it would be a train of death rolling on a railroad of doom and stopping it would be nearly impossible. Surely it would take at least a TES protagonist to reverse that sort of momentum.
Even though the Empire signed the WGC, both sides were left devastated because of the war.
Both sides were not left devastated. Summerset Isle is perfectly untouched and has been for centuries. Cyrodiil was ravaged by war, with the Imperial City taking a huge beating. What did happen to the Thalmor is that they lost their entire invasion army. That's a big blow but it's not a show-stopper. Summerset Isle is still safe, and Valenwood is still a strongly defended Thalmor province. What this means is that if the war had continued, the Empire would have a strong army but no enemy that said army could pounce on. Instead they'd be taking one needle-[censored] at a time from small Thalmor raiding forces, never being able to mount an offense to actually win the war, and during this time the war fatigue would steadily increase until it reaches critical mass and people surrender just to end the fighting.
If the Empire granted Skyrim indepedence and convinced Hammerfell to join them as an ally rather than serve them, they might actually stand a better chance against the Aldmeri Dominion than if they were to continue a civil war and ignore Hammerfell.
The Empire can't let Skyrim go. Look on a map. Letting go of Skyrim would split the Empire in half all by itself, and it would also signal weakness to every baron or lord out there who'd like his own little kingdom. Next High Rock would quit and the Thalmor divide and conquer ploy would still bear fruit. An independent Skyrim is about the worst situation you can imagine for the Empire.
As for a "union" between Hammerfell, Skyrim, and the Empire, please do consider the status before the Great War. Hammerfell, Skyrim, Cyrodiil, and High Rock *was* the Empire. It wasn't enough to mount of offensive then, back when they were one nation, united under Talos. Surely a loose alliance isn't going to be enough either. No, the way I see it, the Empire stands or falls with Skyrim and Tamriel stands or falls with the Empire. For all its faults, and they are many, the Empire is a vastly preferable alternative to the Thalmor, and that is the real decision one has to make when deciding allegiance in the Skyrim civil war.