can my neices choose not to go on visitation with their dad?

No the children do not have a legal right to make that decision. As long as they are not being abused it is a mothers job to encourage a relationship with their father if it is strained. We are the adults and we have to make those hard decisions for our kids. I found that when I made the decision to try and be peaceful with my ex that my girls were much more at ease - they didn't feel like they had to choose. Children need both parents - even if one is a schmuck

In some states the child can decide at age 13. If I was those girls' mother I would contact my lawyer and try to get a visitation restraining order on HER, meaning that she can be no where around when the girls are with their father, Of course you have to document her cruelty whether its mental emotional or even belittling. The only thing is, is that the girls would have to testify in front of her and their father. Been down this road with my own children. If its that bad t might be worth it

the court may consider the 13 yr old but the 10 has no say just yet

He's clearly self centred here and not thinking about the children. Surely their feelings should be taken into account and they given the choice what they want.

Let them say what they want and not what he wants. They will grow up resentful and it will stay with them for life. Surely that is child abuse?

You do not say who the 2 live with which makes the question hard to answer. If they are living with their mother then it's her decision to agree or disagree with her.