Re: Punishments Outside of the Home
I agree with the other posters - if our kids act like that we make them sit away from everyone/play area until they calm down and are ready to act nicely. If he wasn't able to calm down, I would have asked the friend to watch DD so I could take him out to the car, buckle him in his seat, and have him sit in there until he calmed down and, again, was ready to return and act nicely.
I wouldn't worry too much about the screaming - it honestly doesn't bother me, as long as I see a parent dealing with the situation, kwim? It's the screaming kid when no parent is doing anything, or when the kid is acting like a terror and parents do nothing, that ticks me off.
If nothing else worked and he wouldn't calm down at all, I would unforunately have to leave and try again another time. This is a punishment for DD and yourself as well, which is the crappy part. But maybe a trip, just the 2 of you, for a special treat or something would make it up to her.