Maybe it was rare for women to drive in cities but in small town and rural areas it was routine. Among my older relatives some had a driver's license, some didn't. Entirely their choice, or inclination. One had a driving license but never learned to drive. She got it in the thirties, at the police station, by paying a small fee (I think it was 25 c) no test. She only used it for ID.
Another always drove the car because her husband never learned how. She had a series of Studebakers, I remember a Starlight coupe in the early fifties and a 2 tone 1956 Hawk coupe. From the thirties through the early fifties Studebaker was the style leader. Later she had a Chrysler hardtop. She was quite a stylish dresser too, and there were rumors of a rather "sporty" past.
On the other hand, having a second car was considered extravagant until the seventies.