When you are together as a couple with your children's other parent, you have a relatively large degree of control over the people your children are exposed to. However, after a divorce, or break up, it is typical for that control to decrease. It can be frustrating, as many parents new to this situation wonder if they can prevent their children from being in contact with certain people. Unfortunately, unless your ex agrees otherwise, the short answer is no, unless there is a significant risk of harm to the children from said exposure.