This is a long thread but I would like to add something. Since dad has the child in his custody, and since the dad didn't pay child support for two years, I suspect that what the AG is collecting from dad is the arrearages rather than current support. Therefore, in my opinion, wednesday IS supporting the child if she is returning his money to him.
He would owe those arrearages even if he got custody and wednesday was ordered to pay child support. So it really isn't HIS money that she is returning to him, its hers.
I realize that the AG could also be collecting current support as well, however based on the fact that they are already in court over custody, and it was given temporarily to dad, I doubt that current support is involved at this point.