Let him clean up after them, drive them around, pick them up, and wait on them if that is what he wishes to do. So often the second wife starts feeling resentful about the amount of housework she is expected to do when the children are visiting. It's likely his former wife felt resentful about this too. Keep note of this because that is probably what he'll do when you have your own children. It's not that he's a bad man.
Society makes it easy for men to opt out of child care, and house work.
Even today with women's lib and equal rights being expected these types of jobs are often relegated to the women. We women allow it to happen. If you don't want to feel resentful do not allow it to happen. If you set the boundaries in the beginning you're going to be a lot happier when you bring your own children into the family. He'll eventually realize pretending to do it wrong won't get you to do it.