I am going to assume that his country of origin is NOT a signatory of the Hague Convention on International Child Abduction. And as such is under no obligation to recognize the validity of and much less enforce your US custody order.
I am also going to assume that if he or his family has the clout in his country of origin that was alluded to in this thread, that it would most likely be a fairly simple (or rather easy enough to actually do it) matter to obtain passports (and citizenship, of course) for the kids from his country of origin.
Last assumption: it would be possible for him to get court orders in his country of origin giving him full custody of the children.
In this case (assumptions true or become true), he could very easily get the kids out of Mexico traveling on non-US passports with a non-US custody order. Easily. And once back in his country of origin with the kids, you would have virtually NO recourse if the courts in the country of origin do not recognize your US court order. Which they wouldn't, having already issued their own orders and not being in a Hague Convention country.
Then, you'd have a costly and pretty much hopeless battle on your hands in a foreign country, foreign court system, somewhere where your ex and his family have political clout. Where I'm assuming that "due process" has a rather fuzzy/flexible definition compared to what we are used to in the developed West.
There's your (almost) worst case scenario.
It comes down to how much you trust him.
I think you've mentioned enough real read flags given the legal nightmare that could ensue without too much of a stretch of the imagination to say "Hell NO" to your question. And have that not be paranoia.