I am not really sure about him at all; that's the problem. He has problems with substance abuse and mental instability, which make me feel unsafe even though he's never done anything to me. However, he has talked about slapping a previous girlfriend and during our divorce proceedings I found out he'd been arrested for domestic violence with yet another woman. So? I just don't know how to judge the situation.
We were in his country for a few months prior to the separation and divorce and there was a lot of family/tribal violence going on and I saw members of his family do things I would have never expected of them in order to maintain family honor and loyalties to their extended tribe. Again, this was radically different than my first stay in his country so I really don't know what to expect of him or his family members.
He has a nephew who was raised in the U.S. who has been dropping hints about my ex's possible thinking whenever he calls to check on/talk to his cousins. (The nephew is a grown man with children of his own, so he seems more like an uncle to my kids.) The nephew asked if I thought my ex would try to come over the border and I told him it wouldn't surprise me. He said, "It wouldn't surprise me either." The nephew and my ex's brother came to visit the boys last month and the subject of me allowing the kids to go back to their father's country or moving there with them came up. I said, "No, that won't be happening. When the kids are 18 they can decide if they want to go to their father's country, but I won't send them there and I can't live there." I explained that my ex has copies of all the paperwork explaining his rights under the divorce decree and the nephew said out of the blue, "I don't think he'd hurt you." I hadn't mentioned anything about being afraid of him, so it seemed like a strange thing to say.
If we were to go to Mexico, it would definitely be supervised visitation. I wouldn't let him be alone with the kids simply because of his substance abuse and instability. However, I'm not sure I'd feel all that safe myself being with him. I really don't know how his mind is working.
Finally, I know it would be hard for him to get out of Mexico with the kids, but it wouldn't be too difficult for him to disappear with them and make it very hard for me to find him.
My gut instinct is to say no because of all the weird red flags, but I don't know that it would hold up if he took the matter to court. The reality is he likely will never get a visa to the U.S. and I will not travel to his country and am under no legal obligation to send the kids -- at least as far as the U.S. divorce decree is concerned; his country may/may not recognize the divorce.
Thank you for your time and energy on the responses, everyone.