Well, I'm feeling a little sorry for the child as I read your post. Not only does she needs rides, but she also needs friendship (you mention that she's copy-cattish and clingy, and that suggests to me that she needs somebody to look up to). And the older she gets, the more friendship she'll need.
I also imagine that her parents assume that of course you'll take care of all the transportation, since you've always done it. They may not have given it another thought. And why should they?
Resentment is emotionally very draining. I suggest that, instead of steaming, you call the parents and say, in a firm but friendly way, "We love your daughter dearly, but our schedule is getting so crazy that I'm going to be able to give her rides home only on this day and this day. Will you take care of the other days, please?"
I can picture two possible results. The parents may actually come to pick up their child (and possibly yours?) from practices. That's the best hope. The other possibility is that they will tell their daughter she can't stay after school for activities on the other days. Then you will have to decide what your next step will be - let the girl fend for herself or adopt her unofficially. (In the latter choice, of course, you'll finance the gasoline expenditure.)
I've been in situations where I felt as if I were an extra parent, with all the care I had to take of somebody else's child. It wasn't on my to-do list, but it happened. I hope I was a good influence on the child in the end.