Disclaimer: Do not take this as actual legal advice regarding your insurance coverage.

Now that we have that out of the way, we can say that if you are covered by Geico, and your Geico policy covers you when renting a car, and your daughter is listed as an additional driver on both your auto policy and the rental contract, then............she should be covered in an accident up to the limit of your policy coverage for any damage she might do to the rental car as well as liability. That's the way it typically works.

Also, don't forget that many credit cards provide rental coverage and would include any additional authorized drivers on the contract. That coverage might be primary or secondary (obviously, primary coverage is better) but it's an added cushion should you or your daughter get into an accident.

Hope this helps to put your mind at ease.