Have I mentioned the driver insisting upon driving? Where?
I thought it was generally accepted here on this etiquette board that the host is responsible for the guests' comfort. The driver/vehicle owner is the host. As you said, he's not "the hired hand;" he voluntarily has accepted a role that involves the safety and comfort of numerous people. The passengers are the guests. It is crass and ill-mannered of a host to belittle a guest for something as fundamental (and relatively involuntary) as fatigue and sleepiness, or to abuse his power to cause others discomfort while they are confined in his control.
I ask again: If a passenger requested a rest stop and the majority of the group said "We don't need to go, forge on!" -- would it be considered a case of "my car, my rules" (and frankly I've always thought the "my house, my rules," meme to be unnecessarily rigid and black-and-white) and kudos to the driver for saying "Sorry OP but you'll just have to hold it till we get home -- and I'll do some extra swerving around to make sure your bulging bladder ricochets around inside your abdominal cavity! Because I'm just that kind of guy!" Would that be OK, like jostling the OP awake with erratic motions of the car is apparently OK with some of you?
Who on earth would spend a millisecond more than necessary with these people?