I think if she wanted to drive herself, all she'd have to do is say, "Friend, I'm not sure riding with you to the hike is working well for you and me. I seem to be making you uncomfortable when I fall asleep, and I may not be able to completely avoid it. Maybe it would be better for me to drive myself and then you wouldn't have to worry about whether I was asleep or awake?" And he could either say, "I'm sorry for giving you a hard time about that, if you ride with me, I won't wake you up again" or "You know, I think that might be for the best. So let's meet up at Rock Ridge at 9am and don't forget your hiking shoes!" Even if he does say "Oh, ride with me, you just have to stay awake this time" you can reply with, "I'm sorry, but I don't think that's going to work. If you're not going to be okay with the possibility of me dozing off, it's better if I drive myself."
It's up to the driving friend to behave politely too, and if he's going to get upset when offered a polite, considerate choice, that's his failing not the OP's. She only gets to decide her actions, she cannot control his response to them or his feelings about them. But I don't see any option that allows her to sleep in the car, against the wishes of her friends and the driver, whatever their reasons are. If the groups sees the time in transit as part of the outing, and the offer of the ride is conditional on the riders staying awake, it's up to the OP to either find a way to stay awake, or arrange her own travel separately.