In California (and other states are similar) your sister can sell the car while it’s in your mom’s name. She needs an additional piece of paper signed by you, the executor of the estate. In CA it’s REG 5 Affidavit for Transfer without Probate. It’s a paper stating where and when she passed and who can sign for her.
You sign it and the title. You sign your mother’s name and your name next to it. Title and Affidavit are DMV forms signed under perjury of law of course.
Give these signed papers to your sister, and she can act as your personal assistant by doing the legwork for finding a buyer.

Make sure you also sign the release of liability so sister can turn it in after she sells the car. It prevents the DMV from sending future notices about the car to the old address.
In CA we have to get the car smogged before we sell, but I don’t think you do. New Jersey DMV is:

contact the insurance company and update them. Follow their suggestion.