The right to travel is only applicable to travel between states, not to the right to move in and out of the US. The right to travel is not specifically included in the US Constitution (although it was specified in the Articles of Confederation), but is generally accepted and cited in a number of Supreme Court decisions as well-settled law.

While the facts of this case are a bit much, the idea of unfettered movement is problematic - do we just leave the crossing open for anyone to use, citizen or not? Do we have to staff every border crossing 24 hours a day? Or do we have to put troops along the whole border so anyone can cross anywhere, any time?

It's so easy to say what shouldn't be done, but much harder to say what should be done.