She's moving on and seems to be coping, but the kids are still too angry even to spend much time with him. She overheard one child explain to another that it will never be the same again. Of course he blames her for their attitude. It's going to be up to your friend to establish a good relationship with his kids. Trying to convince the kids won't work.
Kids judge, based on behavior.
If your friend calls regularly, sees the kids regularly, demonstrates caring, and acknowledges their anger at him it should help. The addictive behavior gives short-term relief only. That's why the person keeps engaging in the addictive behavior. Often there is more than one addiction. I have had same sex encounters.