Very possibly, she want cash, and she don't want to repair the car too. You don't need to go to the garage with her, I think. What you can do are
1. Identify which damages were made by your car. You just pay for that.
2. Say her estimate is too high and give some examples from you or your friends.
Bargin with her about the ammount of the money you have to give to her.
I think you'd better not to say something like "thank you for your not let my insurance company know", because that will bring you to a bad position to bargin with her.