Skyrim is weakest while the war continues. The Empire has been proven to be unable to resist Thalmor, as can be seen in the capture of their capital.
The Thalmor's sudden invasion caught the Empire off-guard, and so it was the element of suprise that allowed the Thalmor to advance as much as they had. The Imperial city was promptly recaptured, and literally all Thalmor forces in Cyrodiil were destroyed. So no, I don't agree with you there.
The Battle of Red Ring postponed the Empire's eventual defeat by spurring the signing of the the White-Gold Concordat, because the war became too much of a financial burden on the Thalmor. However, the concessions the Empire made in Skyrim, such as allowing Thalmor laws and officers into the midst of their territory, attest to the Thalmor's strong influence on the Empire.
I don't know where you got the whole financial burden aspect from. The Thalmor army in Cyrodiil was completely destroyed. As to the WGC's concessions, they don't point to Thalmor influence in the Empire (seriously? How could you even think that they'd hold any influence whatsoever with the Empire after ransacking Cyrodiil?) but rather to Titus Mede II's (justified if controversial) desire for peace. After the horrendous losses of the Great War, I think that swallowing a bitter treaty for the sake of peace and recuperation is worth it.
The "army of ragtag peasants," if you support them, can defeat the Empire, making them a stronger force in Skyrim, making them more able to stand up to the Thalmor in battle as a stronger military force.
...What? That didn't really make sense, and how each group would fare against the Thalmor is speculation. The only factor was can use to even measure such a baseless claim is the Legion's performance in the Great War, and let me remind you that, despite being caught off guard, it brought in reinforcing Legions from Hammerfell and Skyrim rather quickly and utterly destroyed the invading force.
As for a "united Tamriel," that is like saying that if Rome had conquered the entire world it wouldn't have collapsed, which is highly unlikely and never could have happened.
I don't understand what you mean by that or how it related to Tamriel. Surely you wouldn't argue that the Empire before the Civil War, encompassing Cyrodiil, Skyrim and High Rock, with resources shared between the three provinces, wouldn't be weaker than those three provinces and Hammerfell facing the Thalmor threat alone and divided instead of united under the Imperial banner?
Finally, as a financial onus, the Empire has established its own palace in Solitude and taxes residents to support an army which then spends all its resources fighting the residents that refuse to pay the taxes and refuse to be ruled by the Empire. This "imperial trade" is monopolized by a single company which reaps the benefits of the trade and leaves the suppliers of its trade goods in destitution. This company is also highly corrupt, if you have done the Thieves Guild quest which deals with it. In addition, imperial trade is a mere shadow of what it used to be, with lost territory and no hub of commerce (the Imperial City).
Where does it say that the Blue Palace is an Imperial structure? It houses the High King, leader of all Nords. The one who was murdered in an unfair duel, remember? This entire tax business is murky, because we really have no primary information on it, and how does the East Empire Company leave its suppliers in destitution? Surely Tamrielic-wide trade, eased by Imperial control, would benefit all parties involved? We don't have much information on this though, so you and I both are speculating. I can't say I've played the Thieves questline, so I can't comment on that (no spoilers please!), but I assure you the Imperial City still stands strong.
Look, I'm obviously pro-Imperial and you're pro-Stormcloak, but at least I'm trying to look at both sides of the argument. For example, I never argued that Ulfric is a racist, although I do think he allows too much leeway against Mer in Windhelm. I also strongly dislike the White Gold Concordat, but I understand that, unpleasant as it was, it was borne out of necessity. Things aren't black and white, you know. Neither the Empire nor the Stormcloaks are pantomime villains or heroes.
Edit:
They think he can be useful to them. That doesn't mean it's true. It certainly doesn't throw a bad light on Ulfric's character as you said.
No offense, but I think the Thalmor know what's useful for themselves more than you or I.
As for the character part, I'd refer you to this part:
Spoiler He was made to believe information obtained during his interrogation was crucial in the capture of the Imperial City (the city had in fact fallen before he had broken), and then allowed to escape. After the war, contact was established and he has proven his worth as an asset.
This suggests that he betrayed Imperial forces, though probably under duress, so take that as you will

(I won't blame the guy; torture is torture. But, it seemed to me like he was willing to betray Cyrodiil to save himself).
The first time I read the dossier, I interpreted "established contact" as there being active communication between the Thalmor and Ulfric which was broken off after the Markath Incident. This is partly vague, though, so this is indeed up for interpretation until further clarification.