I carry a blanket to help keep from being "exposed" when changing the lower half.(that's really the only illegal thing involved with changing in a visible location). I even sometimes do the shaving and all the makeup in the car. I get hot water "for my tea" from McD's and use that to shave and rinse with. Then I plug my lighted makeup mirror into a ac/dc adapter and put my makeup on.

And yes, putting a waist cincher/corset on inside a small vehicle is not easy. Much easier to take it off!