S.L.
Wow. It's hard I'm sure. I have 2 thoughts that go through my head about this. One thought is that the kids should have a say and can you ask for a CASA worker to be assigned to them? If they really are unhappy they should be able to say that it's too much and too disruptive in their lives to go back and forth.
BUT..my 2nd thought is that the fact that he is not with his 2nd wife is irrelevant. All kids need to have a good relationship with both parents if possible and he and the kids need to figure this out together. I'm sure he isn't an imbecile. He must love his kids and want them to be around. I'm sorry he lied. Lord knows why he did that. But he probably had friends and family members telling him he would be giving up too much and that he'll be pushed out of his life if he does that now.
I think getting them some assistance would be very helpful in helping them to communicate their own needs. They are too young to be able to say why they don't want to go back and forth and even though you say that you don't bad mouth him in front of them, you can't hide your feelings. Body language speaks volumes.
This is why I hate divorce so badly. Anyone that says staying together for the sake of the kids is wrong because they see too many fights doesn't realize that the fighting doesn't end after the divorce. The fighting just becomes more costly and more complicated with even more lasting hard feelings if the people don't find a way to work it out. I guess in my own life I've always felt that it would be better to put the effort into saving the family without a divorce.
You are divorced from this man but he's still your other half of parenting. You and he need to find a way to communicate and compromise just as much now as you should have when you were married, maybe even more.
Suzi