The Thalmor invaded Valenwood long, long before the Great War. They manipulated Black Marsh even longer ago, and Elsweyr chose to side with the Thalmor. Very few saw them as a threat, it wasn't just the Imperial government that was underestimating them.
So they can't have had a very good spy network. Or rather, it appears to me they had plenty of warning (the Blades, warnings from refugees like the author of
The Rising Threat, and according to
The Infernal City, certain elements of the Penitus Oculatus which were trying to figure out if the Thalmor were responsible for Umbriel) and either chose to ignore it or couldn't muster a defense even of their own territory let alone their provinces. Which is sort of all the point- the empire is an empire only on paper, and very thin paper at that.
I believe in that same conversation it is revealed that High Rock stays on the side of the Empire, or at the very least will not help Ulfric in his rebellion. I find it curious that you have yet to speak on Ulfric's capabilities as a leader. And given the fact that he looks down on anyone who is not a Nord, I doubt very much any alliance that he might make between Skyrim and Hammerfell would last very long.
It's small wonder they would stay out of the Skyrim civil war. It's not their fight. Once Ulfric wins, then they'll have to deal with him. I'm sure it won't be easy- Hammerfell and High Rock both historically have had problems with the Nords, but I don't see what choice they all have.
As for Ulfric's leadership ability, he's more of a general than a politician, but I don't see that he's any worse than the poor leadership in Cyrodiil. And he seems to have a clearer view of the Dominion's threat than they do.