My girlfriend & I had a similar situation on Saturday. We were sitting at Friendly's trying to enjoy our a meal. In the back was a birthday party for what looked like 4-5 year olds. There were a few parents there. There was one little girl who came making this horrible, grating, banshee-like howl over & over. What did her mother do, you ask??? Told her to stop....which lasted for a hot 10 seconds. Even after receiving several evil glances from myself & other patrons, she still kept it up. A few of the dads with the group sat there giggling like it was funny. She eventually shut up after the ice cream was brought out.
If I ever, EVER, acted like that in public, I can't imagine what would've happened. I lived in fear of divine retribution from my father, although the man never laid a hand on me in anger. It was just the thought of what might happen if I stepped out of line that made me behave. That and the fact that my Dad, though only a hair under six feet tall, may as well have been ten feet tall to me as a kid.
Luckily I was blessed with a good kid who doesn't act up in public. I really don't need much discipline with her, but when I use the "Dad" voice, she knows to straighten up.