Wow. I would be completely flabbergasted. Not mad, really, as much as gobsmacked. You would drive my daughter all the way to the farmer's market, punish her by making her leave and punish my other daughter by denying her time with me because YOUR daughter was rude and, obviously, embarassed you? And you don't think that by making my daughter leave you were ultimately giving your daughter what she wanted because she plainly stated that she didn't want my daughter there? Wow. Gobsmacked.
I mean, I can see the other side. The mom was obviously mortified or she wouldn't have done it. And I'm sure her intentions were good because she didn't want your daughter's feelings hurt by her daughters naughty behavior.
I think my response would be, "Well, you are obviously tired because I can't imagine why else you would be behaving in such a rude way. So, for today, we will skip the concert, you can go lay down and rest for awhile and I will play with our guest. Maybe when you wake up you will feel better." Naptime wouldn't have to be a real naptime, just as long as it took for my daughter to feel "rested up" enough to be kind to her friend.
Wow.
L.