Minor fender bender... want to settle with family so it doesn't go against insurance. (See Details)?

Go with the members of the other car in the accidents to a car maintenance place. Get a quote on how much it would cost, talk with the other family if they're willing to do this, pay through card (or some way of proving with a receipt later on that YOU were the one who paid, highly do not recommend paying in cash) and that should be good.