re: Car insurance question

Absolutely not true. Carfax finds out about accidents from insurance companies and police reports. I am in the vehicle repair industry and have never heard of a collision repair shop selling damage data to Carfax. Carfax is a joke. Just another money making scam.
OP - my advice is to get quotes from a few different, reputable, collision centers. Just to make sure you are getting a fair deal. Also ask if they offer any kind of discount, depending on how you pay.
Also, pay out of pocket. Between dealerships using carfax against you when trying to sell or trade your car in, adding your daughter to your insurance, and them increasing your premiums, you will end up paying much more in the future if you go through insurance.