Safe option is always to go with the insurance, that way you're guaranteed to have the work done to an acceptable standard, providing the insurance company allows you to choose where to have the job done.
However, as you mention, you don't want to screw the young fella up for the next few years. If the dad seems sound and runs a good restoration business, then that seems like a good option to me, so long as he doesn't just basically flip write offs on the cheap.
Decemeber 2012 my partner was rear ended (Yeroo) by a young driver. Her dad came down to see the damage the next day after we had a quote at a shop that I was happy with. I'd previously googled him and found he was a school principal, so that filled me wilt confidence that he'd do the right thing. We agreed to leave the car in at my body shop and once it was finished, he'd call over to pay for it and we'll all be done with it.
Everything went off without a hitch and the car was looking better than ever. 3 weeks later we traded in it for a 1 series, but thats besides the point
Personally, i'd give the dad a chance, but as mentioned earlier, check out his business and see if it's the kind of place you can trust to do the work to your standard. I'd also consider bringing the car to another shop to get an idea of whats needed. They may be able to tell you if the hinges are damaged or the frame. Then you can agree to source the parts that are required and he can pay for them, that way they'll have already paid for the part and can't pretend to have replaced it, when they just bent it back.