Riding in a car is very stressful for rabbits, and that's probably what caused him to die. I'm so sorry. It was probably a heart attack and shock. Car rides are so stressful that they are often used to get bunnies to bond--I am trying to bond a pair and in the bathtub they go at each other with fur flying and teeth out. In the back of a moving car, however, they have to lie down for stability and lean against each other for support.
Rabbits should be in small-ish carriers so that they don't move or get bounced about. They should be positioned with their bodies perpendicular to the direction of travel. This is so that the starts and stops of the car don't make the rabbit go flying facefirst into the front of the carrier or such. I have tried it both ways and they are much calmer in this position. I have also tried big carriers, and that's stressful. They should be able to stand on 4 legs in the carrier, lie down fully extended, and if there are 2 bunnies they should be able to lie next to each other. They shouldn't have a lot more room than that. It's also important to have something in the carrier that gives them traction. A bare plastic floor is not good. A towel or even better a best of hay is better. Travel is best done at night, or the cages should be covered to prevent sun from getting in them. Adequate air circulation and good temperature control is important. The carriers themselves shouldn't bounce around. Music in the car shouldn't be too loud, and the driver should be careful to avoid large bumps or changes in speed/direction.
