I am really confused how do you get from Women Driving to children disprecting their elders. One has nothing to do with the other. Driving is just a nessasary neutral act of modern life, no different than turn on the lights, Shall we say women should not turn on lights.
There is no mixed messages about driving, most people do it because its a part of life. In fact most frum women do it because they are carpooling their kids to school.