He won't be crossing the border as a Mexican national but as a US citizen without a passport on him. The secondary is implied since they'll have to do the database lookup and verification process to determine if he is a US citizen. The legal issues will add to the bad experience, but with the options available, it's the best one by far.

OP, keep in mind that the best case scenario for you on a trip like this is a massive hassle getting back into the US. You will have zero sympathy from CBP on this. In fact, they will make it as hard as possible for you, with the idea that if you can afford a trip to the PI, presumably a hooker run, then you can afford to pay off some of your child support. Since you were presumably on a hooker run to the PI, anticipate having your cell phone/tablet/laptop inspected and possibly seized for forensic inspection since some of the hookers might be underage. I would not rule out a body cavity search for drugs either.

They will make your life very difficult as you are circumventing the lack of a US passport due to legal issues. In their eyes, you're a deadbeat dad who won't take care of his kids. Expect to be treated as such, even if it's not the real situation.