When speaking of rental car insurance that one typically buys as part of their auto policy it is for the use of a rental car or rental car reimbursement if you have an accident or insurance claim so that type of coverage would not cover you "renting" a car from a person whose home you were renting out.

That being said many car insurance policies will extend your actual auto insurance coverages to a rental car when you rent one for pleasure due to being on vacation, etc. So you could be covered under your own insurance policy for rental cars but normally this is for a car rented at a standard rental car agency not one that you are renting from an individual. You would need to speak to your agent to see if your policy would cover this "rental" vehicle or not.

The person renting to you their vehicle also needs to check with their insurance agent to see if their car insurance policy will cover you driving the borrowed the car since you have their permission. Usually when you borrow a car the car owner's insurance is primary and your insurance is secondary but this rental situation is a bit different than letting a friend borrow your car to run an errand.

The transfer of insurance to a rental vehicle used for pleasure varies by insurance carrier and by state law. There are companies that will allow the transfer of insurance to a rental vehicle for any purpose; others will only transfer it the rental vehicle is being used as a replacement vehicle while the covered auto is out of commission for repair or due to a claim.

Your policy declarations should explain how and if coverage transfers and to what extent. You mentioned that your policy does transfer to a rental vehicle; you may wish to clarify the coverage afforded under your policy for such a situation as the definition of a rental car may be specifically outlined by the insurance company. There are differences between a borrowed vehicle and a rented vehicle with regards to the laws in each state and to the insurance coverage extended with most insurance companies. The car owner should also contact his/her provider as well to ensure that there is proper coverage for the vehicle during your vacation.

For a definitive answer, refer to your policy. If it is unclear, contact the license agent that issued you the policy. They should give you a direct answer for your situation regarding your auto insurance coverage per your policy. You will have to refer to an attorney to determine the contract laws in the state where the vacation house and car are located to find out if a rental agreement is necessary for liability and insurance reasons and the lawyer may also be able to determine how insurance should be placed on the vehicle for you to be covered.