Re-read the early quest. There's several times (very early on) where Ozai only partially had a stick up his arse and just seemed happy to Dad. At a guess, I can only presume Azulon kept pushing and pushing him like he's pushing Akane, and now seeing his children with (approaching) healthy relationships who don't want to kill each other is setting him off.
Like, take Akane's interest in the other schools of bending? Ozai initially approved of that and helped her out. "My will is my sun." is something he taught her.
He was already a bit of a bastard at the beginning, but it's clear he's been making a descent into greater bastardry over time, rather than just starting out always maximum bastard from day one. Stick insertion has been a gradual thing.