One issue can be that the original material has somewhat dried-out (the base oils in it) as it aged. This is normal. Gentle heat over a period of time, with possibly some good vinyl conditioner (NOT an ArmorAll-style lilquid!) could help restore some of the original pliability to the vinyl. This will take some time, so multiple gentle heat/conditioner applications might be needed. Of course, benign gentle in handling the vinyl is necessary, at all times.
Leather would have been only on the seating surfaces, NOT on the door panels. The vinyl would be grained to match the hides on the seating surfaces, typically.
Of course, you could also get some close-match vinyl from a quality supplier and replicate the original designs into it. The faux stitching could easily become REAL stitching, for example. This might be the easiest-to-do option. But it would be nice to restore what you have and reinstall it, too.
You might get some of the white polyester padding to put under the vinyl for a bit of pad. Just a thin amount, though, for a little additional "body" to the vinyl. Rather than it being glued to the board.
Of course, you can make new watershields out of some heavier clear plastic sheeting.
Just some thoughts,
CBODY67