To those who say she should have driven, not flown, that is unfair. Driving and gas is expensive, and a drive like that would have taken several days, sometimes over dangerous terrain. Perhaps this mother works and only had a certain amount of time off. I think those who do not have children, or forgot what it is like to have children just don't understand.
I live on the west coast, our entire family on the east. We have to fly to see our family. My son, fortunately, is a great little traveler, and we have flown MANY times. I can only remember one single time that there was a problem with him. When he was 18 monthes old, we had to fly to AZ for our househunting trip, and we had first class tkts. The first leg of the flight my son cried and was very fussy, but by the second leg he slept. This trip could not be helped---we had to find a house. We could not have driven, we had time constaints with our jobs. Everyone has a right to purchase airline tickets, parents cannot always help when their child are not feeling well or is fussy, you do the best you can. People around them could learn to be more compassionate and tolerant of lifes little inconveniences.
As far as compensation, FWIW, one flight I took with my son when he was one year old, got cancelled due to weather. It was later in the evening on a Sun, most of the restaurants etc in the airport were closed, and I only had one extra diaper, and a small jar of baby food. We waited HOURS until USAirways decided to completely cancel the flight (they were hoping the weather would clear). I had limited funds at that time, in a city where I knew noone, and my husband was 600 miles away. USAIR finally decided to put us up in a hotel because they said we were not allowed to sleep in the airport, and I was finally able to get some food for my little one. I am thankful USAIR provided the hotel accommodations, I do not know what I would have done. I quickly learned to carry more provisions when I traveled, in case of emergency, but at that time was a niave young mother. I often wished that there were vending machines in airports with diapers, baby food, and other supplies for children. Traveling with children is not easy, and neither the airlines nor airports make it easier, but sometimes it cannot be avoided.