Recently, I got into a car accident. Someone hit me from behind, which was not my fault. I opened a claim and request insurance to provide the rental car till my car got repaired. Since, I have a rental coverage in my personal insurance policy, Insurance people are saying I don’t need to have a separate rental car insurance. Here, I am kind of reluctant to use my personal insurance in the rental car. I am kind of scared (may be because of the recent accident) that if something happened to rental car, rental guys will claim and my premium go higher. Is this typical that we must use our personal insurance in this type of situation or we can ask for separate insurance for that repair period?

Yes as long as you have a full coverage in your insurance you may not have to buy extra insurance.Depends on your coverage limit. Also you may have to pay for the rental which will be reimbursed at a later date .

You should go his/her insurance company to get rental and file claim with them. Why you want to use your insurance, if the accident was not involved your fault?

When I had accident and my car was being fixed, I didn't have to pay separate insurance for the rental car (as long as my car was at the body shop). I didn't have to pay for the rental either, the insurance company did. Later my insurance company was reimbursed by the other driver's insurance company as it was not my fault.