I think it sounds like her husband does the school run for her when he's able to. But I wouldn't necessarily have an issue with it working the other way either. It's fairly common around here for husbands to be a substitute in daycare.
I hired an older student to walk my daughter to school. Unfortunately I still have to pick her up myself at the end of the day. If I was in your situation I would just ask each family which way they prefer, nice and warm in the van vs. In the wagon, near you at all times.