key word being distant.Such as that ruler burning and raping them?
I mean, her going through that and deciding for herself that such treatment can't be right doesn't sound too far-fetched to me.
Also, you have a poor understanding of the mind. Abuse doesn't lend itself to anger unless the abused had some significant degree of pride and sense of self-importance relative to the abuser before the abuse, and the abuse just started recently. Anger is a kneejerk reaction. Ozai is much more important then a servant. Also being a servant probably doesn't give her much to be self-important about.
Keep in mind that in story thus far, Akane was closer to Ozai then to Ursa, up until recently, and then the sparring incident happened, so she might know she's on thin ice with him and thus not want to risk sneaking out and getting caught.