There is NO deductible under liability coverage, in other words, (her car) and insurance pays 100% for her damages. And yes would be owed a rental car while the car is in the shop, thus your insurance would pay for that also.
But, how do you know if the amount (estimate) to fix is the right amount or not? Your insurance company has people who review the estimates to make sure not overcharged and will pay (only) the right amount. Also the rental car, that most insurance will only pay (X) amount, but if she gets one much higher, then you are on the hook. Plus, if the car is held up in the shop, then (your) insurance will deal with that, since many times a body shop may have too many vehicles to fix, thus they work on the ones that have to be fixed sooner, thus if not, then they go after the body shop to fix it and cut down the cost of the rental.
The question is, why does she want you to pay vs insurance? It is possible she wants the check, but does not fix it and that is ok also, but if she does not fix, then you don't owe for a rental car also. Or, if you file the claim, it is (possible) that your insurance finds that you are not at fault, or that they find that (both) of you are at fault, thus they pay less.
Signing a waiver still won't prevent her from coming back later for injuries, since any good lawyer will throw that out, thus you need your insurance to handle, just in case.
You have accident forgiveness and yes if a 2nd accident happens, then get "dinged" but you may not have that 2nd accident, thus file with your insurance company and let them handle it.