I believe that in some jurisdictions, men can be thrown in jail for not paying child support. Here in my country, men are compelled to pay, and they cannot refuse to pay on the grounds that their wives won't let them see the child.
To me this isn't right. If a man is under an obligation to pay child support, because they are his children, then he should also get visitation rights. His children are, well, his children, and by virtue of this, he is entitled to see them.
Either a man isn't on the hook for child support, in which he won't get to see his kids, or he is on the hook, in which case he should get to see his kids. The state and the wives shouldn't be able to have it both ways.