No, you don’t need to drive a car with dual controls for your driving test!
On the day of your test, your examiner will require the following:
As long as your mom’s car has these things, you should be allowed to use it for the driving test! Keep in mind, though, that your car will typically be inspected by the examiner before the test begins. They will make sure that both of your front doors open, you have all of your mirrors, your lights work, and that your horn is functional, among other things.
If you’re worried that your car might not pass the test, check your state’s requirements on the DMV website prior to your exam.