No. Your daughter is excluded from your car insurance policy, so your full coverage does not extend to her accident.
If you were driving and wrecked your vehicle, your collision or comprehensive coverage would cover the incident depending upon how the accident occurred. You simply would pay your deductible and have your auto insurance provider pay the remaining due for the repair of your vehicle or its actual cash value if it were declared a total loss.
When someone drives your vehicle who is listed under a named driver exclusion, then there’s no coverage whatsoever.. This is even if the excluded driver operates the vehicle in an emergency situation or takes your car without your knowledge. (See “Excluded really means you’re excluded”)
A child taking your car without consent wouldn’t be considered theft, which your comprehensive coverage would normally cover. Instead, it would be considered unauthorized use, which makes it another reason the insurance company wouldn’t pay since coverage benefits only cover permissive users.
When you exclude a driver on your policy, that individual isn’t rated on the policy, thus saving you money on your premium. In return, your car insurance company won’t extend coverage to that person if he or she drives your vehicle. In simple terms, you didn’t pay to have your daughter covered by insurance and so your insurer will not pay for the accident she was in with your vehicle.
I suggest you lock up car keys if you have an excluded driver in your house, particularly a young one. And while you won’t be able to get your car insurance policy to pay for the damage to your car, you can seek compensation from the at-fault party — your daughter.