We took a different route with our daughter. Binned off our old second car (MX5 - after it got written off when a caravan broadsided it parked outside our house), got an i10 and put her on my insurance. She was off to Uni 18 months after passing her test anyway and didn’t need her own car for that, and only wanted access for an occasional social drive in sixth form.
Told her if she had an her-fault accident or picked up speeding tickets she’d be back on foot/the bus, and to be fair she’s avoided both so far (5 years later), and we keep the same arrangement. It’s rare that all 3 of us need a car at the same time when she’s back home, as she is now, even though we live rurally, so it’s rarely a problem (but guess who goes without when it does happen...

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Still have the i10 which we bought new, which is a great little run around, and not caused us any grief or unexpected expense. I usually choose to use it over the “main” car (BMW X1).