A small idea, we know that the fire nation is royally fucking things up and probably pissing off more than a few spirits with their antics. What if Azula and company (Ozai's Angels, etc.) had a run in with a spirit who had been running amok. Azula gets taken to the spirit world, perhaps before or during the time she is hunting down the gang, and learns a bit about the balance of the four elements, and learns that a lot of things they are doing now will only end up haunting the Fire Nation for years to come. She begins to learn about the balance of the four elements and how killing the air benders screwed it up.
After being rescued by Aang (she was but one of many), she reflects a bit on this, and finds two key points. One, the spirits care about the benders as a whole, so the practices of hunting down benders and killing or putting them in concentration camps will only damage her power base due to the retribution by the spirits and likely lead to numerous rebellions. Two: the spirits don't give a damn about politics. Which, in Azula's mind, is a free pass for her country to conquer the world. She realizes that the various peoples would have a hard time willingly joining the Fire Nation due to various character flaws (in her view). Resistance is inevitable, but self interested groups might find it better to join the Fire Nation, if properly motivated.
So, we have an Azula who is trying to conquer the world through treachery and deceit. Ba Sing Se would go differently, as Aang is kind of necessary alive at this point, however dangerous he may be to her; though, it's doubtful she wouldn't try to manipulate him to putting himself in a position where he can't stop her. Zuko never gets the chance to reconcile with his family; though, Mai would still probably visit him, and might try to help him in various ways.
Eh, not the best, but any thoughts?