If it's the bank wanting to see proof that your son is incurring expenses, that's !@#$% BS and just tossing another obstacle to prevent the money from leaving. Or is it the cousin wanting to see this (can't tell from your phrasing, but none of his business either.) You shouldn't have to prove anything except that the son is the legitimate owner of the money now.
I'm coming around to the opinion that the best way to deal with this is for you and your son and a Wuhan relative with signature authority, go in person to the bank as soon as you've arrived, deal with a bank manager, and oversee the sending of the wire transfer, refusing to budge until it's done. Or get the money out either in a cashier's check (pain in the @ss) or USD cash (painful only if you lose it). Bringing it back to USA isn't an issue as long as you declare it, just keep all the paperwork as to its provenance.