Zuko getting back to the palace really late after a whole day of outside business and little Izumi staying up to wait for him but he expected her to be asleep so she ends up scaring him half to death in the dark
Imagine little Izumi being incredibly excited for her first day of school and getting ready extremely early and it wakes Zuko up so he finds her on the porch totally ready to go and he’s like “It’s still 4 in the morning please go back to bed”
What if Mai died in childbirth? And once Izumi found out the real reason her mother wasn’t around, she blamed herself and believed that she had caused her father nothing but pain, so she runs away in hopes of letting her father finally be happy. But really, Izumi was what made Zuko more happy than anything, and losing her completely destroys him.
Headcanon that Izumi would sneak in and hide in the throne room eaves dropping on her dad’s meetings when really Zuko totally always knew she was there because frankly she was clumsy but he played along to keep everyone else from noticing
Zuko is the kind of dad that would take on his daughter’s date in the absolute most passive aggressive way possible by being extremely friendly and welcoming in person and then glaring judgingly from a distance whenever Izumi isn’t paying attention