It is comprehensive coverage that usually covers damage done to a vehicle due to a run-in with an animal, such as a deer. It does not appear that this was part of your insurance policy. Since you are the owner of the vehicle it is your insurance that is primary on the vehicle. If it does not cover the damages then it could fall onto your daughter's insurance policy to be the secondary or excess if her policy permits.

To find out if either insurance company will pay for the damages or medical bills you will need to contact both of the insurance companies and get specifics regarding your policy coverages.