If you are worred about him leaving with her---something called "risk of child abduction"--then you shouldn't let him have visitation at all.  Period.  None. If he wants visitation, he will have to file a family law case called a parentage action and seek a visitation/child custody order.  If he does, then you need to tell the judge about this risk of child abduction.You should speak with a local family law attorney and seek help.Best of luck.