Nightowl1, obviously it's entirely up to you guys how you proceed, but I think not using your insurer is a mistake. Once liability is admitted by the third party insurer your insurer will be working on your behalf to get the best outcome for you. Otherwise you have no one in your corner. What happens if you're not satisfied with the repair, they can assist you etc. If liability is accepted by them (how can it not be given the video), your son will make a full recovery of the excess, indeed he may not have to pay it out initially either.
As for future premiums, negotiate & shop around. I had a claim 7 years ago after being hit in a car park whilst at work, no idea who did it & no witnesses or video. I had to have a new drivers door, total cost circa £1k. My premiums have remained fairly static since, I'm paying about £20 more than 5 years ago.
Good luck whatever you decide to do.