A.: I don't necessarily think of your wife's comment as an independent thought. Her idea that she should not drive sounds particularly old-school. I wonder what lies beneath her comment. It could be that she truly does believe that women shouldn't drive, or at least that wives shouldn't.
More likely, she has a fear of driving. If she hasn't driven before (which is common for New Yorkers who don't need a car to get around), she may feel unsure of her driving ability and skittish about getting behind the wheel with her children.
Probe a bit to find out what the real issue is. If she is nervous about driving, giving her a car may not be a viable option.