Read the Lore.
Hammerfell is its own sovereign Kingdom. They refused to accept the WGC, and thus seceded from the Empire while the Empire at the same time kicked Hammerfell from the empire for refusing the WGC.
*** This is all from the Official Lore/Cannon as well. ***
Hammerfell has a mighty distrust of the Empire right now, but they fought the Aldmeri Dominion, lead by the Thalmor, to a stand still and forced all of the Aldmeri forces to leave Hammerfell.
The Redguards are not looking to "rejoin" the Empire at all, and hate the Empire almost as much as they hate the Thalmor. Unless Ulfric wins the Civil War and Skyrim secedes from the Empire, don't expect any help from Hammerfell against the Thalmor.
The redguards are back to doing their own thing now, and they are perfectly happy with that.
Yes but no one said that the Redguards have to join the empire again, we've just been stating that they would be allying themselves with the Empire because they could see that it would be a good way to destroy the dominion which they hate more then the empire where as we have no actual evidence that what Ulfric says about attacking the Dominion is true, we just know he says it to encourage his troops.
That would be crazy, it would be more beneficial to deal with the Redguards as they sailed or marched down towards dominion territory then to force them in another war. Deal with the Empire, worry about the Redguards if they come, and not before. Because if they would do what you suggest then they would automatically be fighting the Redguards and they would be fighting on two fronts.
The second option could be considered a breach of the WGC and would leave Cyrodiil open. The third option is probably the best but incredibly risky, Talos help you if the Redguards decide not to join you or even worse decide to take advantage and take over white-gold.
Redguards wouldn't attack cyrodiil, they wouldn't be able to win if they did and it would just weaken them leaving an opening for the Dominion and though they hate the empire there no proof anywhere stating they hate the empire more then the Dominion.