Because the damage is minor, it's probably best not to involve your mom's car insurance company. I would recommend having the at-fault party get an estimate for the damage (which they would have to do anyway) and pay for the damage out of pocket. Because a car insurance company would charge you for any at-fault claim (which this would be considered as) for 3 years and the average increase in Texas is around 40%, the damage most likely costs less than that premium increase. If the other party isn't interested in going around insurance companies, you are obligated to follow suite. If that's the case, here
is a step by step guide on handling the process.