By federal law you have to be 14 or over to have a non farm or hazards work place job. States can have that as older, like in California the last that I knew you had to be at lest 16 for a non farming job.
Show business has its own child labor laws that has nothing to do with any other industry.
Having your own children working for your own company there are no restrictions as long as its not defined as hazards work. It has been known in the past when child labor laws where first passed that people would adopt children so as to have a free labor force. Such adoptions had been stopped decades ago.