Back Child Support even if child is no longer living with parent?

My brother-in-law recently moved back home with his girlfriend who is 18. She's pregnant, and he's out of work. The other night we talked about her mother still collecting $300 dollars a month in back child support from the 18 year old's father. Shouldn't the 18 year old be the one getting the back owed child support, and not her mother? They could probably use that money for their needs right now. If she has a legal right to that money, how does she get it?