[Cadaverous Pallor]

When he talked to the kids on the phone, Grandma didn't want to talk to him. It may not be much, but I think it's an indication that she does not like him, either because she actually thinks he's a murderer or just disapproves of his current lifestyle (the way Michael Caine does).

If that's the case, then getting into the U.S. doesn't help him much, since Grandma would still not want him to see the kids.