I think the "broader question" is are national child labor laws constitutional?
For the sake of argument, I will acknowledge, reluctantly, that Congress has jurisdiction and power for such a federal law emanating from the "commerce clause" (when did a "foreign nation," or "one of the several states" or "Indian tribes" become a private business?), but such power has to respect the Bill of Rights.
Amendment IX
The enumeration in the Constitution of certain rights, shall not be construed to deny or disparage others (rights) retained by the people.
Is not the decision as to whether children work or not a right "retained by the people," or their parent(s)?