I do not know the customs of the community to which he belongs according to your letter. I do believe, however, according to that which I have heard, that they completely oppose the whole idea of a woman driving a car. Although other pious communities have a different view on this matter, nevertheless there is the well-known Torah principle that "In the place of Rav, one is to act according to the rulings of Rav; in the place of Shmuel, one is to act according to the rulings of Shmuel."

Excerpt from Igros Kodesh, Vol. XVI, p. 203