Can a parent be stopped from seeing their children if they do not pay child support?

No. The right to child support and access are separate legal issues. They are both rights of the child.

A parent cannot be denied access to their child because they have not paid child support. And a parent might still have to pay child support even if they do not have access. For more information, see CLEO's resource Separation and Divorce: Child Custody, Access, and Parenting Plans.