On what grounds? It's a very simply question. Did the Court reach the merits of Miller's argument or not?
The court cited the law of the case doctrine, so you know that they didn't rule on the merits of this case. So what? Their ruling still binds the lower courts to the custody/visitation order of the Vermont court.
And, the Vermont court followed their statutory law. The child custody has been determined and the Virginia Supreme has ruled that determination is binding in Virginia.