I'm not a parent...
I have quite a low tolerance to minor noises, minor irritations such as people who can't wait a a counter without rat-tat-tatting their credit card or coins on the surface, or those who have to constantly clank the side of their glass with finger rings in pubs etc., yet loud unavoidable noise I can deal with (even sleep through quite often).
Screaming, or tantrum-throwing babies and toddlers can be very trying, but they are a fact of life.
I was flying Dublin to London (45-50 mins maximum), and had a middle seat; by the window was a "Very Important Lady", and in the aisle seat a Japanese lady with a babe in arms. All was well until the engine note went up on the take off roll, which is when the tiddler started squealing - cue daggers from the VIL. The lady with the baby had very limited English, and in between efforts to comfort her child was attempting to signal apologies to those around her. Not good enough for our VIL, who spent the whole flight shaking her newspaper very loudly, exhaling equally loudly, tutting, and "For God's Saking" for the whole duration of the flight.
The lady with the baby just couldn't calm him/her down and was in tears at one point herself. On landing the baby calmed down as soon as the engines were wound down, but VIL was only just getting properly wound up. The sort who un-clicks her seat belt the second you turn off the runway and starts the "Excuse me I need to get my things for the locker."
One of the FA's gave me a tap on the elbow as I was getting off and said "You picked the wrong seat today eh?" "I don't mind, babies cry." "Maybe, but adults have a choice how much noise they make." Gave me a grin at the end of a crappy working week.