i'd definitely check hips. unless you clearly see fear there shouldnt be any reason your dog cant jump into a car (being an overweight 120 shepherd who gets tired just looking at other dogs run doesnt count).
my old dog only jumped into the back of the suv when he was hyper and really really wanted to and had a running start. other than that he'd put his front paws up on the seat like you described. he had hd + he was fat. my healthy dog could jump in the back of a pick up at 6 months old.