Basically, you want to hold up the bankruptcy court while you go get a child support order. But, at the moment, there isn't an order, and the BK court can't give your new order retroactive priority to the date before the BK filing (at least, I can't imagine how that would work).
Or, maybe you want to ask the bankruptcy court to rule that the divorce judgment claims some "equitable" amount of support, and therefore the court will liquidate that amount in fairness to the child.
In either case, you would be opening up the federal courthouse to making child support determinations, and a flood of new litigation. I think the judge will trot out the abstention doctrine and send you packing.
The solution to S1's problem is to go to the family court and get a real child support order and hold S2 to it. And, if S2 doesn't pay, then S1 files for contempt and gets a money judgment for arrears and then executes/garnishes S2 and his property, and/or has S2 doing community service/jail time for failing to pay support or seek work, etc.
Note: I do admire your zeal, but I think it's a waste of $10 for the parking garage.