Just a thought... you might check into which countries participate with the U.S in returning/locating "kidnapped" children (the Hague convention, I think it's called). My dh and I have 3 children - my ds, who was born in the U.K. while his father was in the military there, his dd, who presently lives in the U.K. with her British mum, and our ds.
Being a military family, I *know* there will come a point in time that we travel internationally with the kids. I have less worry, knowing that my ex can't exactly run off w/ my ds without going AWOL, but knowing that the government has programs to help return children is helpful as well.
Going overseas is a fantastic opportunity - I *hope* that my ds has the opportunity to visit his grandma in Korea, or his uncle in Japan, his birthplace, etc, whether it's with me & dh, or his Daddy & (step)Mama.
Oh, and I hold his passport. I like that too, LOL.