Yeah, I talked to Mugshots just now, and I even suggested that no company that does business legally (whether in good standing or even of ill repute) would EVER send payment to someone through an unknown, third-party acquaintance whose job was not that of an escrow or something of that sort.
From the sound of it, the hangup with PayPal was that they flagged him for trying to send $1500 from an IP that isn't familiar to his account. That isn't exactly unbelievable if you've ever worked with PayPal before. They're a nightmare.
I suppose I would suggest this: Several smaller payments through PayPal. Say something like $250 every Monday and Thursday for three weeks. That would total $1500 paid without being such a high amount as to hang up PayPal.
If not that way, then even a direct transfer to the father's bank account. Or, hell, the OP could just go out and get a bank account tomorrow. This is the United States. It doesn't take long to do. I've done it over a lunch break.
That would honestly make all this go away it seems. I don't blame Mugs for not wanting to send $1500 via Western Union to a third-party alleged acquaintance of the person he's trying to pay. The request of such is shady as hell, and nobody who knows what they're doing would EVER do that. The fact that the OP is requesting it is absurd.