What she wants the money for is irrelevant honestly. This comes down to what people think a parent's responsibility is when paying child support. Should that parent have to pay what's necessary for a reasonable lifestyle for the child or should that parent have to give the child enough to fund a lifestyle that would be comparable to what the child would receive if living with that parent. If it's the former, that chick doesn't have a leg to stand on because there are few places in this country where $6500 is insufficient to take care of one adult and one child. If it's the latter, she might have a case because a lot more than $6500 would be available for the child CB was the primary guardian.
If I were in these situations though, I would ask if it was possible to get some kind steward that took the child support money and ensured that it was spent on the child in a responsible manner. I don't see why anyone should assume that the mothers in these cases will do the right thing with the money.