I feel one of the scariest things about Ozai is not necessarily the physical abuse he pulls on Zuko or Azula. It's the mental abuse and how under the radar it is.
Yes, it is easy to look at Zuko's scar and be horrified by his abuse. What I feel is more effective was that Ozai made Zuko believe that he deserved it. That he had to go on this three-year odyssey to try and find the Avatar for a chance at gaining his love back. Their reunion isn't about Ozai apologizing. It's Ozai saying how proud he is of Zuko for making up for HIS mistake. He doesn't mention the Agni Kai at all, and when Zuko does turn, he tries to make it sound like some exercise in learning respect.
Same thing with Azula. Ozai puts the mantle of Fire Lord on her shoulders, effectively giving her the responsibility of running a country. He puts on so much pressure to have her to be perfect (pitting her against Zuko, sending her out on missions). The only approval that he gives is for her performance which reflects on him. Basically, he treats her more like an asset more than as a person. And any failing she makes is on her part.
He puts so much responsibility on both Zuko and Azula, but never takes any for himself. So if they displease his high expectations, that's their fault.
And they believe him.