Fence it all in except for the side facing Mexico. Put people there. If they want to stay, they can. If they want to cross into Mexico, that's between them and Mexico.
Effectively it becomes an extension of Mexico, except that Mexico has no say on the people we put there.
This overcomes the problem of us rounding up people but having no place to send them - in those cases when the recipient nations won't take them.
Of course Mexico might decide to build a fence on their side. And pay for it. Which Trump can then claim is a fulfillment of his earlier promise.
Let's see . . . 12 million divided by 1402 acres = 8559 people per acre.
That's 5 square feet per person. No sanitation. Should be a good incentive to move on.