Saying "your kids have to go to school and not work" and then paying the adults 3 dollars an hour. The family winds up making more money without the kids having to work. (in this admittedly limited example, the family makes double)
If you take the kids out of the equation without increasing the parental pay, then yes, you'll have a harder time with things, as the family just lost 66% of their income, which will mean cutting back.
So you are correct that it is complicated and "stop kids from working" isn't the FULL answer. But it doesn't mean that there aren't solutions - plenty of countries have child labor laws without falling apart.