Triplese7en asked: What if Ursa didn't left but Zuko still got banished? Would it change anything (and would it change the Zucest)?
If Ursa is able to, she's gonna kill Ozai, and then she and Iroh will just say Zuko isn't banished anymore. Since A LOT of bad shit has happened, and Azula cheered while Ozai disfigured him, she and Zuko won't be on good terms for a long time. However, with the main reason why their relationship started falling apart being finally gone, they'll slowly start rebuilding their relationship. Considering they're both going through puberty at that moment, they're gonna have lots of very confusing dreams about each other, and eventually the temptation will be too great for them to resist. Needless to say, that will help them like each other a bit XD
If, for whatever reason, Ursa doesn't kill Ozai, it could possibly lead to her finally seeing that being Ozai's favorite child isn't all that much better than being the unfavorite. She'd be more supportive and protective of Azula, and while that wouldn't be enough to fix everything, it'd make the situation easier for both of them. Once Ozai sent Azula on that mission to capture Zuko, Ursa would beg Azula to try and help him capture the Avatar so he'll be allowed to come back. But since Azula would be afraid that Zuko coming home would mean that Ursa would go back to neglecting her, she wouldn't help him…
Until Ba Sing Se. Interacting with him again - even if it's in a rather negative context - made Azula realize she missed him much more than she had previously thought, and then things play out mostly like in the show… except that once they're home, they'll be fighting both for their father's approval and their mother's. Azula feels inadequate because Zuko told Ursa that she almost didn't help him so she's very disappointed in her, but because she grew closer to Ursa during Zuko's banishment, Ozai no longer sees her as the perfect daughter/ weapon. Zuko feels insecure because he is no longer the sweet, kind boy his mother loved so much, he is constantly afraid that his father will find out that his "accomplishment" of killing the Avatar didn't actually happen, and on top of all that he also feels guilty for having betrayed Iroh.
However, being home, even in such a bad circumstance, shows him that he didn't hate his sister as much as he thought he did, especially since her kinder side is showing a bit more due to Ursa's influence. That ends up making them turn to each other for support despite their rivalry still being very much alive. They'll probably end up in bed together once they're sent to Ember Island, and once that happens and finally something feels right, even though they know this should feel so completely wrong, they just can't stop. On the day of the eclipse, they're leaving their nation and taking Ursa with them.
The poor woman and the Gaang are going to be very horrified once they walk in on them and find out how exactly they "bonded"