I've seen my daughter on the other end of this kind of playground drama. I've heard other kids tell her that they don't want to play with her. I had hoped that she wouldn't be the one doing the pushing or hitting, or whatever it may be, but she was, and, really, I shouldn't be surprised. She was too impatient to wait her turn to jump off of said mat thing, which the girls had all been doing in rotation, so she pushed the girl. Just that simple.
For once, though, I felt surefooted. I knew exactly what to do: we checked on the other girl, we removed my daughter from the situation, waited until she calmed down, I apologized, my daughter apologized, and we were out. Activity done. There was no hesitation, no "maybe I should let them play some more," no embarrassment on my part, no shaming lecture for my daughter. Just an efficient resolution.
And it's a good feeling that, should I ever be on this side of things again, and I no doubt will, that I know just how to handle it.