State laws and insurance companies' guidelines may vary but yes, it is normal for an insurance company to require that all licensed household members must be listed on a policy as a driver or excluded.

If you are listed as a driver there usually is a rate change, so here it would be the $20 extra dollars a month for insuring you on the car as well. Insurance companies are normally permitted by the insurance regulatory body to consider all resident operators of an insured vehicle in the rating of an auto insurance policy. So even though you may only occasionally use your girlfriend's car, you still use it thus the insurance company wants to have you on the policy and rate accordingly.

If you are excluded from the policy the insurance company is correct that there would be no coverage extended to you at all from her policy if you were in an accident in her car. Since insurance normally follows a car first and driver second you would not have primary coverage from her insurer if in an accident. While you do have insurance of your own, your insurance company may not want to cover as secondary insurance since you were aware there would be no primary coverage due to being excluded.

Your girlfriend can cancel her policy with her current insurance company if she is unhappy with their service however most all insurance companies will want you on her policy since you reside in the same household. She may be able to find cheaper insurance though now that she is aware you will need to be listed on her auto insurance.

You may also want to check with your insurer to find out if they require you to add your girlfriend to your policy or if your policy is okay as it is. To get insurance rate quotes for your girlfriend, you or the both of you - follow this link for discount auto insurance.