My DD threw out her H after two affairs one New Year. She was always determined they would have an 'Andrew and Fergie' type of relationship, and that is what has happened. It was a struggle at first, but now her Ex sees the children several times a week, they stay over at his house, and they even spend a few days away together (separate bedrooms!) for the sake of the children. Christmas is spent with the four of them together. The children have coped very well, for them it is normal, they don't favour either parent. My daughter keeps her thoughts about her ex, who also left her £30,000 in debt, to herself, and occasionally us when the children are at school!
If they work at it, and it sounds as though they want to, it will work out okay. Sadly their situation is so common that the children won't feel left out at school.