If I look at it strictly in terms of child labor, there's nothing stopping those opposed to child labor from leaving Virginia and/or discriminating against products made there. Just as we can today with products produced by brands that we know use child labor.
What? That's not what I said at all. In fact, as I initially said, "Please don't think I'm in any way arguing for child labor." How can I make it more clear?
My point is, in the hypothetical situation that a state did allow child labor – which I do not at all condone – people could choose not to buy products from that state, as people already do in not buying products from certain brands and countries that use child labor.