No sympathies here. You can’t control your children so that they do not cause headaches for the rest of society, they will turn into arrogant yabbos that feel that everyone else owes them something and deserve only their sneering contempt. I speak from experience, and no, no child I raised has ever been allowed to throw a tantrum of any sort. They may have started to, but they learned very quickly that the results of any such actions brought down upon their heads repercussions far outweighing any momentary glee they might have experienced from their oh-so-unwise actions.
One can make accomodations for an infant, but for a bratty two year old there is no excuse. It is a manifestation of bad parenting skills, period.
Frankly, in this day and age and all the TSA, DHS and other travel ills, the last thing we need is have to put up with brats that their parents should know how to control. Just because you download a kid and want to travel somewhere doesn't mean you get to make other travelers' lives miserable. The right decision was to throw the family off the plane.