So both kids are with you at all times, while H is out of the house? In other words, he's abandoning his kids -- both biological and step-child -- while he's out with his OW?
His son is only with us every other weekend. On those weekends he has been staying at the house, although not very active -sleeping in until late afternoon, not wanting to go out and do anything.
If he has plans with OW he will just cancel picking up his son for the weekend, as he did for thanksgiving. The kids were both pretty hurt by that because they were really looking forward to having the holiday together.
During the week when it's just my daughter at home, he will stay at the house 1 or 2 nights a week, sporadically, but usually shows up right before her bedtime.
He says once he is fully moved out and gets all of his belongings out, that he will only be at the house on weekends when he has his son so that the kids can be together. And once a week he will come over to have dinner with my daughter but not stay over. Who knows if that's even true. Probably not.