Oh dear, this thread has brought out my PTSD symptoms. I have had two horrible flights with children - my own. The first was when we were flying from Melbourne to Bangkok about 15 years ago when my perfectly behaved, easy-going, quiet 18 month old child cried the whole way, for no apparent reason at all. I did everything I could think of to no avail. It was incredibly stressful and embarrassing, even though as far as I recall no one made a comment or even gave me a look. To cap it all, the minute we landed he fell into a deep sleep and had to be carried along with loads of luggage all the way through Bangkok airport (we were moving countries). Thankfully Thai attitudes to children are kind and the officials fast-tracked us through queues for immigration etc.
The second time I was flying back from Spain to England with a very stinky toddler. I looked and looked and could see nothing in his pants. I concluded he must be farting for England, so didn't do anything else till we landed. His daddy discovered the errant lump at the airport.
Until my youngest learned to read he could be quite difficult on flights. He's extremely active and being forced to sit still for long periods of time with nothing to do is torture to him. Even now he can't sit and watch a film all the way through, he'll be up and down all the time. On short haul flights without seatback screens it became a challenge to my ingenuity to keep him occupied. I used to take a small dvd player for the flight itself and boxes of soft fruit for the ascent and descent when all electronics had to be turned off, and slowly feed them to him, hoping the seat belt sign would go off before I ran out of fruit. But I do recall on one occasion having to hold him screaming in his seat until the seat belt signs were turned off. Luckily those flights were for British holidaymakers, so were full of screaming kids anyway.
As a result I have a lot of sympathy for parents of crying babies on flights and will offer to help if I'm sitting nearby. But I can't recall ever being really bothered by other people's children. Maybe I've just learned to screen out the noise. A couple of years ago we took a big trip that entailed lots of night flights, and at those times I was driven nearly frantic by people talking through the night. I think that's far worse than children, who at least have some excuse for being annoying and inconsiderate.