“Exactly what would he do to stop a private group from doing this? This is the problem many of us have with Trump. “
Probably use the bully pulpit like Teddy Roosevelt. Public pressure can do a lot.
A President can also make crossing the border inconvenient. I got turned back from Mexico during Nixon because, to quote the Mexican border guard, “your hairs are too long”. It was just some ruse to cause problems at the border,
I never did find out exactly what the real issue was at the time but it wasn’t hair. Instituting time consuming rules to gum up border crossings would be very easy and doesn’t require any new power on a President’s part. If it takes the better part of a day for golf pros and fans to go in or out of Mexico, Trump will get their attention.
...and they'd better bring in their own water....LOL!