I'm not sure specifically what the 'car mom story' is. It could be about a mom's experience related to a car, like her daily commute in the car, or perhaps a special memory involving her car and her family.
The 'car mom story' could cover a wide range of things. It might be about a mom who is always in her car shuttling kids to and from various activities. This could involve her experiences dealing with traffic, having conversations with her kids in the car, and how the car has become a sort of second home for her. Or it could be a story of a mom who had an adventure while driving her car, like getting lost and then finding a beautiful new place she never knew existed.