Re: Ex married his affair partner. Now she doesn't like him to be away from her.
It sounds like he's not strong enough to stand up to her. It's always the kids who get hurt the most in something like this. See a Family Lawyer. If he really WANTED to see them, he would. I would go for sole custody. A good second wife would understand about the kids and at least ride it out until they are all 18 and be good about it. If you have insurance to cover counseling for the kids, I would seek it for them and for you, too, if you feel you need it.
Re: Ex married his affair partner. Now she doesn't like him to be away from her.
Agree that is sadly common. I think you continue to try to do what is best for your children as many women do, suggesting in a nice way that he visit, and trying to make arrangements as easy as possible. Sometimes you do what is right in this world. People get divorced but someone who tried to keep a father from his children is not a nice person, and when you marry such a person, karma tends to get you.