What if, instead of banishing him for refusing to fight, Ozai banned Zuko from ever firebending again? He still grows up in the palace, but was never sent to find the Avatar. Instead, that duty fell to Commander Zhao.
Now, the gAang are in the Fire Nation capital, trying to find Aang a firebending teacher.
Notes:
I’ve been into Zukka fics lately, so I MIGHT go that way.
Also, Azula still cares for her brother, and they both hate the Fire Lord. Ursa was killed.