To comment on the debate between tapping the brakes versus tapping the sleeper, the idea of a driver taking on unnecessary distractions from the road, no matter what form they take, bothers me, I will admit.
If a driver taps the brakes when there is no road-relevant reason to do so, I suppose it might or might not cause an accident. It might even if it was a light tap, because brake-tapping is used as a communication device with other drivers, who might misinterpret your intentions and act accordingly and set off a chain reaction. It's possible, but the really basic fact is that the driver is, for a moment, not focusing on the road-he's more concerned with whether or not that passenger is sleeping and therefore distracts himself.
If a driver reaches back to tap the sleeping passenger, I don't know if that's better or worse. To do so quickly would require taking one's eyes off the road, even if only for a second. And we all know what a second can mean on the highway. To tap a sleeping passenger *without* turning around would mean a random fumbling in the general direction of the back seat, possibly for several seconds. Still looking at the road, yes, but with a distraction that could mean serious consequences.
Honestly, I think that if a driver has genuine objections to people sleeping in the car, especially if this poses a safety hazard to that driver and especially if it's not okay if just one person stays awake, it is really really important for that driver to always make that known when offering a ride to anyone. That way people who know they are likely to fall asleep can decline. And arrangements can be made regarding if someone who usually doesn't fall asleep does, how will they be woken up? Because falling asleep in a car can happen even to someone it's never happened to before, as we know. Other passengers can be alert to if anyone is falling asleep and can take care of it so the driver can focus on the road.
So, I guess my point is, if the driver in the OP really had a problem with sleeping passengers there was a better way he could have handled it. And if it was just a "I can't sleep so you can't either" thing, something that didn't really pose a hazard and he could have easily lived with, though his circumstances weren't exactly what he would have wanted, he was childish and petty to distract himself from the road just to wake her up.
IMHO of course and as usual.