To get right to the point: child labor is nowhere mentioned in the U.S. Constitution. The children's advocates who are discussed in the attached article believed that they would be the driving force who authored the "22nd Amendment" and brought to an end the brutal days of child laborers, but this is not the case (the 22nd Amendment instead ended up being the amendment that restricts a president's service to two terms). This is fascinating read, however, about the scourge of child labor - who was for it and who was against it. A year after this article appeared, Congress passed the Fair Labor Standards Act, and all was well with the world.
More on Child labor laws during the Great Depression can be read HERE...
Yet, regardless of the degradation of the Great Depression, the United States was still an enormously wealthy nation...
More about Child labor during the Great Depression can be read here.