If you and the other driver agree to settle outside of insurance, you would pay for the damage yourself. When agreeing to this, make sure you both sign a written statement and take pictures of the damage. Calling the police can solidify any accident details as well.
Before agreeing to settle without insurance, ask the other driver to get an estimate of repairs. If you can’t afford to pay for them out of pocket, go through insurance. While your mom’s rate may increase, the damage would be fixed without issue.