My MIL had given up driving before I met her but following her husbands health deteriorating and him having a heart bypass we suggested she took a refresher course and start driving again as it would enable her to get about more easily if he was in hospital or just too unwell to drive her places. We paid for the refresher course, and she did drive a little for a while, but he wasn't keen. If they visited us (about 70 miles each way) he would insist on leaving early to avoid driving at dusk. She often suggested that she drive since she wasn't bothered by the light conditions but he would say "It's too far for you to drive." Eventually she stopped driving again and now as a widow is dependent on friends to give her lifts or public transport - not ideal when you live in a small village. I think it is very common for men to prefer to drive and limit their wife's use of a shared car.
My own husband always drove most of the time when we were out as a family and only asked me to drive on very long journeys if he was tired, or on a night out when he wanted to drink. Although I always had my own car and drove every day locally, I became nervous of driving longer distances, especially at night, as I was no longer used to it. After we split up, and subsequently divorced, I got my confidence back as I had to drive long distances to see my family (200 miles away) and children who both went to University at a distance. Some of my colleagues comment on the distances I drive and I wonder if they are restricted by their husbands. I now visit my daughter by train since she moved to Scotland as the journey is too far for me to do without an overnight stop, but otherwise I still drive everywhere. Unless money is tight I'd never suggest giving up your car as it may result in a loss of independence. I don't think either my FIL or ex husband exerted coercive control but were just typical men who prefer to drive than to be driven unless it suits them on a particular occasion.
As far a s the OP's situation is concerned, there may well be cause for concern. Listen to your gut feelings and make sure your DD knows you are there for her. However, men restricting their wives from driving is much more common than you may think!