You are learning the hard way why so many people advocate how wise it is to put your affairs in order during your life to avoid such profound hassles after
If the car payment is the only thing that is left unsettled, you may consider contacting the company that issued the check to explain your predicament. There is a chance it will have a form and format for you to follow.
But you will probably be in for a bit of legwork and paperwork, which may be worthwhile if the check is for a large amount.
Unfortunately, the only person that can legally cash that check would be the personal administrator for your mother's estate. Since she did not name one in a will, you or some other person would have to go to the local probate court and ask it to issue you the authority in what is called "letters testamentary."
To get this permission, you would need to present a copy of your mother's death certificate, complete some paperwork, and pay a court filing fee. You will likely need this authority to negotiate other transactions after your mother's death -- for example, changing title to stocks and bonds she may have owned.