You would not need rental car coverage. However, whether or not you have coverage would depend.
If you loan your car to someone else to drive your car, they can be covered if, you have a permissive use policy, they do not drive your car more than once a month, and they do not live in your house. Also, they cannot be listed as an excluded driver on your policy. If any of the pre-mentioned situations are not true then they will not be covered to drive your car. When it comes to you borrowing a car, you would be covered for any damages that you are liable for. If you cause damage to the car you are borrowing, then those damages would not be covered by your policy. Good luck and if you have any other questions, don't hesitate to ask