This is a horrible way to deal with disagreements within the family…using the kids as pawns. It’s immature, emotional blackmail and frankly disgusting.
Do your best to ignore the coldness and see the kids as much as you can. They are innocent in this and won’t understand if you suddenly drop out of their life. But if they make it impossible to see them…well then honey, you’re going to have to be patient and realize that it’s not you, it’s them.