Hmmm...seems like there are two issues here. The first has to do with whether your reaction to him right now is "reasonable" or "acceptable," and the second has to do with whether your AH is really remorseful, etc. I imagine the two issues are intertwined, and that you might feel like you should be nicer to him if he is really remorseful.
My experience has taught me to separate those issues. Whenever my AH acts remorseful, I'm sure he IS remorseful in that moment. But the remorse isn't lasting, and it doesn't do anything to actually change his behavior. I try very hard to detach from those short-term remorse episodes. Long-lasting actual behavioral changes are what matter.
As far as your reaction to him, I say do whatever preserves your serenity the most. If you are afraid that interacting too much with him will cause you to blow up at him, and you want more time and emotional distance to work through your feelings, then you absolutely, positively have that right, regardless of how "remorseful" he is. If you are avoiding him and "punishing" him because you think it will somehow drive home your feelings and make him change...then you might want to take a hard look at your actions. I can be very cold and distant from my AH. I have to check my motives a lot, because there are times when I do it to punish him, not to protect myself. And yes...with kids, you DO want to limit the household tension as best you can, but not at the expense of your serenity.