The real reason for the ban against chassidish women driving?
Forget what some Nshei Whatever said. They probably said whatever they said for public consumption amongst the masses of gentiles and secular who don’t understand one iota of Torah, tznius and yiddishkeit. The main (but perhaps not only) reason is Shulchan Aruch. Specifically Shulchan Aruch EH 73:1. Shulchan Aruch says a woman’s place is at home and that a wife should not go outside too much. If a woman is a licensed driver and has a car at her immediate disposal to fly off to wherever she wants, there is no question that she will be spending much more time outside of the home than she would be spending outside of the home if she is not a licensed driver.
If you don’t like Shulchan Aruch or think it is no longer relevant or applicable in the 21st century, then I can’t help you.