My H has not apologized for the A. He's still in it! He has said, "I never meant to hurt you. You are my wife and I hurt you."
He has not recognized that the kids are hurting because of his behavior. His rationalization there is that his parents fought all the time and they should have D'd. It would have made life more peaceful for him and his bro. I replied to that one with: My parents fought all the time and then D'd and still fought. Pre-D was better. AND H and I didn't fight...disagreed yes but fight??? Like abuse each other?? not til monster appeared, and then it was pretty much one-sided.
I started telling the kids 2 years ago, (DS13, DD16, DD19 now) that dad was depressed, like a mental illness like Grandma has, and he needed to work on it by himself. I saw their questions were leading to self-blame, so I did fill them in OW and more info on depression and infidelity. When they saw me not taking responsibility for his behavior, it helped them to not do so. (I didn't know about MLC) This did not happen right away but over a period of a year where H was back and forth. They have been most hurt by his neglect and focus on OW. It is hard to explain why, if his behavior has nothing to do with them, why does he ignore them. Now, 7 months into this S, their expectations are zero. They watch ME!