Dear Kristen,
Your issue is a valid concern. I would never want my 6 y/o to travel unaccompanied anywhere, much less from a foreign country! I believe most airlines don't allow it at that age. Regardless, as a parent I would not want my kid going through that. My teenagers have flown with escorts and they made them miss their flight due to sheer apathy and incompetence. And they were talking to them!
She is not supposed to interfere with the father's visitation. If you do nothing though, she probably will be able to travel with him. Your husband needs to hire a good lawyer now to put a kabosh on this right away. Do not delay. Best wishes and God bless!