Vicar, my father has been in a wheelchair for the past 53 years & they do have folding chairs available. I don't mean just the ones that collapse (they all do that!) but actually fold in half once you remove the leg rests, arm rests & collapse it. It might be worth doing some searching around & see if you can find one. Do a search for Everest & Jennings & you'll have a bunch of links pop up!
Many of todays' chairs are very lightweight (aluminum & such) & wouldn't be an issue in our cars.
Best wishes for the missus!!!!