I don't get why people bring toddlers on a plane. DRIVE.
I have a rule, if it's over 8 hours, i fly. Sorry if that offends you, but driving from NY to LA isn't really an option.
Ya screaming kid is one thing. If they're doing just a bit on landing or whatever that's kinda just how it works and everyone should deal with it. If they scream the entire flight then the kid or your parenting is probably just a piece of shit. But changing a diaper on a seat is a willful act of negligence for the consideration of others. F that shit and F you for being a shitty douchebag parent and traveler.
Blatantly obvious that you do not have children. That is exactly what people who do not have children say, and then quickly realize how effing stupid it was when they later have them. Sometimes, they just cry. Drives me up a wall when they do it, but I can tell you as a father of 2, that sometimes, it just happens. Best thing you can do is try to calm/distract them, but there is absolutely no sure fire cure for it, and it sucks balls when pricks like you stare at us. We know. We hate it too. Short of a frontal lobotomy, heavy sedation, or just knocking them unconscious, they aren't stopping.
Also, changing a diaper on the seat is perfectly understandable. The bathroom is way too small on a plane, and will only scare the child more, making the task impossible. Any parent with any experience can change a diaper there and keep the seat, etc clean. It's not that hard.
Also, get over your kid phobias, gheez. You and everyone else complaining sound so childish and soft it's ridiculous. It's poo. Wash your hands. Move on. It's not like you probably aren't picking your nose or scabs/scratching your ass/playing pocket pool constantly. You are probably nastier than the kid.