Hammerfell might want their territory back which the Nords took when they invaded High Rock and Hammerfell during the reign of Uriel VII in the Imperial Simulacrum. They may or may not do it, would be a perfect time to do so, Skyrim is weakened after the Civil war and up for some taking. Redguards are the most naturally talented warriors in all of Tamriel.
It isn't as easy as simple Diplomatic relations, the Stormcloaks have forced many non-nord merchants out of business who will have to close, I doubt they'd all of a sudden be all "Hey, so about the rebellion... no hard feelings." They do execute Tullius if they win, which to be honest he would of been a good bargaining chip if I was wanting independence. They seek to remove ALL Imperial influence, that would include the EEC, which brings so much needed resources into Skyrim.
"When we're done rooting out Imperial influence here at home, then we will take our war to the Aldmeri Dominion" Which I find rather interesting, on how they plan to get to the Aldmeri Dominion, unless they plan to like sail there.