There is actually a labor department explainer sheet on this situation. You have a horizontal joint employment situation:
https://www.dol.gov/whd/regs/compliance/whdfs35.htm
OT: "Under the FLSA, each of the joint employers must ensure that the employee receives all employment-related rights under the FLSA (including payment of at least the federal minimum wage for all hours worked and overtime pay at not less than one and one-half the regular rate of pay for hours worked over 40 in a workweek, unless an exception or exemption applies). Furthermore, joint employers must combine all of the hours worked by the employee in a workweek to determine if the employee worked more than 40 hours and is due overtime pay."
You can have multiple rates (one-child or two-child, for example), but nothing less than minimum wage, and all hours over 40 are 1.5x the applicable rate.