They got kicked out of Whiterun for causing trouble, not for being Redguards. If that's not what you're talking about, what makes you think they distrust the Redguards?
And if the Empire wins in Skyrim, Hammerfell gets no support for sure. And the Empire would help Skyrim recover, true, but would still be focused on itself. That is the biggest problem with Empires. Cyrodiil first, the provinces second. Just like for Ulfric, Skyrim first, Tamriel second. Markarth's silver goes to who controls Markarth. If Skyrim were to be invaded (unless they went by sea, that would be difficult) would the Empire risk leaving their border undefended? Or would they use the weakened Legion that defeated Ulfric to defend Skyrim and leave the rest at the Dominion-Empire border? Then again, I can't see the Dominion just attacking Skyrim, because Cyrodiil would just attack Valenwood.
If the Dominion invades Cyrodiil at the same time, would Skyrim matter to them beyond Legionarres? If the Forsworn aren't gone, Markarth's Nord population will be. The Imperial City would be the most important thing to defend, not Skyrim.
It's the way various NPCs talk about redguard culture. The curved sword comment is amusing, but it shows how out of touch nords are with the redguards. Distrust might be the wrong word. Still, I do think Ulfric would have a degree of respect for the stalemate the redguards managed to achieve against the Thalmor, but as I mentioned before, I just don't believe he could afford to spare any men to defend Hammerfell. Valenwood and Summerset Isle have an immensely strong naval presence and might well take advantage of that fact.
The Empire might 'focus' on Cyrodiil but they would not neglect to rebuild Skyrim as a strong nordic force is beneficial to the Empire. Conversely, a Stormcloak victory would do absolutely nothing for Cyrodiil (or High Rock) and while Skryim might fare better than Cyrodiil in the short-term (in part due to its geography), with the realms of men divided, the Thalmor can turn their attention to whichever province they like, without the looming threat of cross-provincial reinforcements jumping in to defend anything.
I think the only way any resistance works is an alliance of equals.
And this is why there will be no alliance.
Ultimately, the Thalmor will win unless something unprecidented (Daedric involvement, Akaviri entering the battlefields, a domestic resistance within the Dominion etc.) happens. Since Ulfric
and Tulius can prevail, we know that something must come to shake things up in order to validate all those who played, rather than just those on one side. The most logical option is the Thalmor, since they're a known powerful presence we can only deal with on a limited scale in the game itself.
Besides Thalmor domination provides the background for a much more interesting story than an alliance. Ah, I'm getting off topic a little. Too meta xDD