pulled up the drive

It just means to drive. One could infer it means slowly, because you provide two examples in which one would choose to drive slowly, or be forced to to so by physics--but "pull" in reference to a car is just another way of saying drive--it may derive from horse-drawn wagons, which would have been "pulled" somewhere, but i don't know that for a fact.

It just means to drive.

Thanks, Setanta. A superb answer.