I was with my daughter and we were in his truck and fathers, as I drove, I got support and it was a man in a Lexus behind him smashed the front of his car. Should I make a statement, even if its my fault?
And is it possible for her mother to get my insurance to pay for it?
The insurance for the truck is the policy that is at fault for the damage you take and you were paying drove the truck. You are obliged to cooperate with the insurance so that they pay the claim. If you refuse to cooperate, they can (and likely) to refuse to pay the claim for damages. If this happens, the owner of the Lexus or his insurance company after you directly.
Select the plate and deliver the statement. You must take responsibility for your actions. It is much easier that way. Do you really want your girlfriend of the father in his difficulties with insurance?