I do think nodding off is something that the OP can't help and is not rude for doing so. If the OP intentionally curled up for a nap because she thought the conversation was boring, then that would be rude. Some people's bodys shut down when they are exhausted, and they fall asleep whether they mean to do so or not. I am one of these people and have fallen asleep against my will at various awkward times (including when I first met my future in-laws). I agree with the PP who said if somebody is asleep in an awkward time or place, they probably don't mean to be asleep. People have pointed out that nobody else in the car had fallen asleep, but not everybody is the same and has the same energy levels. To use another example, if somebody has a condition such as diabetes that causes them to need to eat more often, should they be chastised for eating just because nobody is hungry and needs to eat.
I do think the OP should either make an effort to stay awake or arrange other transportation if riding with this group. Personally, I think the rule of expecting nobody to fall asleep in the car is silly and controlling (although I can sympathize with the driver if everybody is asleep). Despite how the OP feels about the rules, she should abide by the group rules while in this person's vehicle. I also think it would be rude for the OP to continue riding with this group if she knows she is likely to fall asleep because it seems to be a grievous offence to this group. If a driver had a rule about going 5 hours before making a rest stop, I would think that rule was unreasonable and silly. However, I would be rude to agree to riding with him and then demand he stop every 2 hours. Just because he has a rule that I think is silly doesn't mean I should break it. Personally, if I had a group of friends who gave me a hard time about something that was causing them no harm and that I could not help, I would reevaluate the friendships.