Dear hyperactivepineapple,
I am so sorry for what you have suffered. What a terrible betrayal, to have your OH cheat when you were so vulnerable. 6 months on, you have a new baby, still grieving your father and now this to deal with. I hope you don't mind me adding you to my prayers.
When I was cheating, I was intensely selfish. I try not to be judgmental about myself when saying this. I was a terribly hurting person. The thing about terribly hurting people is that they can hurt other people, even worse than they are hurting themselves, and they are so self-focused that they literally don't see or even imagine other people's pain. For me, my BS didn't really exist as a person with feelings or desires or hurts while I was cheating. I was so self-focused that nothing much existed.
Your husband may not identify his cheating as rooted in being terribly hurting, but I think that there was something going on inside of him that erased you. Unless he is a sociopath or enjoys seeing other people suffering, it's not that he pondered what you were going through as a new mother or the daughter of a dying father; he likely didn't think about it at all, or hurried his thoughts away when he did start to think about you. Now that he's actually thinking about you again, I'm not surprised that he is apologetic. I hope that he is able to work a bit harder on understanding how he got to the point of engaging with an AP in the first place, so that he can fix up whatever was in him that made that seem like a good idea.
Take care, I am sorry for the loss of your father, and I hope you enjoy moments of sweetness with your baby.