From what you have told us it seems your daughter has neither finacial nor mechanical sense. You have helped her out with repairs and now she is asking for the loan of your car.
Either you have spoilt her rotten (oh, leave it to Mummy, dear) or else she really has got a brass nerve.
If you lend her your car, she should pay the insurance.
I would tell her to scrap that car and sell it to a junk-yard, and to use public transport or a bike until she can afford a new car, or else buy one on hire-purchase.
You may not be able to use your car yourself for a while, but that need not, if you change the insurance, preclude anyone with a valid driving licence driving you whereever you want or need to go while you are recovering from your op.
So tell her, sorry, dear, no-can-do. I need the car.