Have you ever had a work situation like this before?

I was thinking about this recently while watching a program on social structures in animal populations. This particular situation happened a few years ago but I still wonder a bit about it. I apologize for the length.
A few years ago I was working in a classroom with a couple younger women (I was 25 at the time and they were 19 and 21 respectively). We were all instructional aides. We had the same training, same job description, same rate of pay, etc.
Part of our job could be considered unpleasant. We worked with a student population that are often not potty trained at 5 or 6 and so they need to be changed from time to time. It is icky, yes. But it has to be done. In addition to that, we had a strict schedule that had to be followed during the day. This schedule depended on weather and so when it was rainy, had to be adjusted accordingly.
At any rate, I set up the schedules for the day following the normal pattern. Another staff member who I shall call "Lila" got snippy about the schedule. She felt that the order of activities should have been done a different way. I told her that this was the standard way it was set up and if she had a problem with it, she could take it up with our supervisor.
She spent the rest of the day snarking at me at every turn. Lila whinged and kvetched about having to do diapers. She complained about how put upon she was for this, that, and the other thing. She and I were scheduled to do diaper duty and she was nowhere in sight. I did the best I could on my own but I was fast losing my temper with her primadonna act. Everything was a grand tragedy and I was tired of picking up her slack. This isn't a job that you can let things go undone either. I had had enough at that point. I announced that I would NOT be changing 15 five year olds by myself EVER again and that she needed to get over there and help. She made yet another rude comment.
So I laid into her. I told her that she needed to knock it off and grow up. Everyone here had to work and she was no exception. If she didn't like it, well, then don't let the door hit you on the way out. It was NOT fair to everyone else that she squicked out on work and then complained incessantly about it. I was sick and tired of it.
Granted, this was not my finest hour. Looking back there was much I could have done to alleviate the situation without resorting to chewing her head off.
But the strangest thing happened after that day. I came into work the next day to find that she had brewed a pot of coffee. She greeted me with a smile and said, "Hi! I made everyone some coffee. Here are the mugs and there is some flavored creamer in the fridge." After that day, we got along beautifully and she was never snarky or complain-y about work again.
Has anyone encountered this before?