A stay-at-home mom should have access to her own vehicle whenever the family budget can reasonably support it, and that has little to do with luxury or convenience. A dedicated vehicle gives her a practical way to handle appointments, errands, school activities, emergencies, and ordinary life without waiting for someone else to come home.
The arrangement also changes when children enter the picture. A household can manage perfectly well with one vehicle until a sick child needs a doctor, a prescription needs picking up, or a spouse gets stuck at work while the minivan sits in the driveway. Suddenly, that second set of keys looks less like an extravagance and more like a very useful piece of household infrastructure.