Can I prevent my ex-wife from moving (possibly overseas) with my 3-year-old just because she remarried a man in the Navy?

You really can't stop her since she has a legitimate reason for moving: to live with her military husband. What you can do is make sure you have an agreement regarding visitation with your daughter. I'm assuming you have an agreement through your divorce. If so, you can go back to court and ask for a modification of the agreement to reflect the changes due to your ex-wife's new husband. You can specify terms such as when your daughter can come back to the U.S. and stay with you and for how long (if she moves overseas). The base being 3 hours away shouldn't really affect your visitation but you can still make provisions for who brings or picks up your daughter, etc.