As you can read in this article, you'll find that child labor throughout most of the Thirties had not been eradicated fully and was very much alive in some of the more brutal parts of the nation. That said, you might be surprised to know that the proposed amendment to the constitution concerning the ban on child labor (18 and bellow) has never been ratified by the Congress even to this day. When this column was written the proposed amendment was already nine years old and the politician who penned it held that the legislation was similar Prohibition in that it attempted to impose a moral code upon the American people. He believed that this was matter best left to the states; he further pointed out that the recently passed National Recovery Act had abolished child labor by fiat (and when the NRA was invalidated by the Supreme Court in 1935, child labor abuses increased a small degree).
Child labor was finally brought under control with the passage of the Fair Labor Standards Act in 1938.
More on 1930s child labor can be read here...