Amy Alkon relates the story of a woman and her screaming 2-year-old son, who were thrown off a Southwest airlines flight (before takeoff) for causing so much noise. Southwest eventually apologized and gave her a free flight voucher. Alkon expresses my own opinion:
I know, I know -- because I am not a parent I cannot possibly understand how hard it is to keep a child from acting out. Actually, that probably has more to do with the way I was raised -- by parents I describe as loving fascists. As a child, I was convinced that I could flap my arms and fly, but the idea that I could ever be loud in a public place that wasn't a playground simply did not exist for me [...] It really does come down to this: Your right to bring your screaming child on a plane ends where the rest of our ears begin.
There have been times when I've had to leave a public place because my daughter was out of control. It's inconvenient, but my screaming kid is my problem, and other people shouldn't have to put up with her noise.
A parent has a duty to deal with his/her misbehaving child. No one else does.