A child acted like this when we were out to dinner the other night. The mother didn't care and the friend of the mother was there with her own son and seemed pretty embarrassed that the mother of the girl wasn't doing anything about the bad behaviour. At one point I turned around because the girl was smacking her baby sister in the face and making the baby scream. The Mum of the girl had gone to pay and the other Mum with the son told the girl of sternly just as the Mum of the girls came back. She said "oh.. what's happening?" the mum of the boy told her and she just turned to her daughter and said "oh that's not nice" the girl hit her sister again, who screamed again clearly upset and smacking the highchair with her fists herself... and the mum just said "hey! I told you that wasn't nice" then continued to start a random conversation with her friend! wtf! poor baby sister .
I think that parents who allow this behaviour are doing a great disservice to their child. Kids need to have boundaries and know what is appropriate to do and not do.
I would be like other posters and if *my* DD's acted like this, I would be horrified but very worried about their health for them to act so out of character. So I would take them home, tell them how wrong it was, and also book in to see a doctor to make sure their outburst isn't related to something physical or more serious.