There is no law that would prohibit you from sending the money back to the boyfriend once the child support office sends you the money collected from him.
If your children are getting public assistance from the state, the state has the right to offset some of the assistance against the money collected.
So long as there is a court order or administrative order of child support, the child support office will keeping collecting the money as specified in the order.
If the child is living in the household of the boyfriend, that likely is a valid reason to have the child support order re-examined.
Your boyfriend should review his specific facts with his attorney to find out his legal options.