My cat also hates the car! They really do like their homes once they get comfortable there.
My most recent trip to the vet with my (one!) cat was an ordeal. She stayed there for three nights.She is back at home now, but two and a half weeks on is still being very fussy about her food, and I think the experience really did traumatise her.
I can't imagine having to do that with three adorable fur-balls all at once.
After the second one, it becomes a little more mechanical, but they normally arrive at the vet a little stressed after several days, have you tried giving them a little pheromones or catnip to make them feel more at home?