J.K.
If the child was born here, and they are married, I doubt she'll be able to take him out of the country without a notarized letter of permission from him. In fact, my cousin, who has joint custody with her ex-boyfriend, can't leave the state of Washington (nor can he) without a letter.
He should put that stipulation in the divorce decree/parenting plan. I think a judge will look favorably on it. It's hard for a man (unfortunately) to get full custody even if the mother is not a great mom. The system is usually biased towards the mom, but he will still have rights and should be able to get joint custody with a requirement that the child stay in the USA with a good lawyer.