Check with your insurance company. All policies are not the same, and not all are accepted by rental companies. Ask the insurance company what you are covered for when renting a car. (I always check at least two, and sometimes three times. Some do give out erroneous information.) Get in writing exactly what it is you are covered for when you rent a car. Show that to the rental company, and they will tell you which overlap and which you will still be required to pay for. You can do all of this by email (or over the phone) before you start your trip, so that you will not have any nasty surprises on your arrival. If you are going through a consolidator, check with them.

Lifey