I'll offer a perspective. I'm a father of 3 young kids (4 year old twins, 20 month old). I often find myself in situations where I also need my children to stop whatever they're currently doing and pay attention to me.
You mention this happened on a sidewalk. Cars drive next to sidewalks. The American culture of cars is the number one cause of anxiety in my life as a parent to young children. I do not want to feel this anxiety, I do not like how it makes me react towards my children, who just want to play and have fun and explore the world and try to understand it. But cars exist. And today they are a much bigger problem than they were when I was their age, for a whole variety of reasons that are very well understood and articulated by people far more intelligent and capable than I am. And my children are, practically every single day, within 4-6 feet of cars that are a) much larger than they have any right to be, and b) driving much faster than they have any reason to, to the point that if they are careless about where they are, or what they are doing, they run a very serious risk of being killed.
That is why I sometimes respond to my children the way that I do, in line with what you've observed here. I don't like it, either, but it is what it is.
Now, I go out of my way to get my kids into big, wide, safe open spaces on a daily basis, and I will deliberately ignore them (within reason -- I keep tabs on where they are, etc.) so that they can go off and find interesting ways to play, hurt themselves, whatever. But I still have to engage with the automobile problem multiple times almost every single day of our lives.
This is 99% of it (other 1% is fear of other parents scolding you). There's a beach bike path near us with only one street crossing in 5 miles. My 6 and 7 year old are free to explore the whole thing unattended provided they avoid that crossing. It has playgrounds and all kinds of stuff they can stop their bikes at.
But I won't let them cross the street we live on because none of these drivers are thinking about pedestrians and even if they were I doubt any of the lifted trucks could even see a 4ft tall kid.
I didn't mean to make it seem like I was challenging the parent's decision to involve themselves in the behaviors of their kids. I'm speaking more to the curt, evidently anxious outburst rather than a more even-handed and considerate approach.
I've screamed at my kids when not looking both ways crossing the street. If not, there is a decent chance they could get run over by an Amazon truck. I don't sugar coat it for them - they know they could die if it happens. After once or twice they stopped doing it, but if it ever happens again Captain Insano will make yet another appearance, whether people are watching or not. But do not fret, as they get 1000x more love.
I never had nightmares at all until I had kids. Now nightmares consist of cars, Amazon trucks, parking lots and the occasional lake or pool drowning.
Anyway, without full context of what was going on in that family's life you saw, I'm not sure if anyone is able to make a fair judgement on what was more considerate, even handed, or whatever. Five minutes before you saw them they could have almost been hit by a car or something.
IMO situations that require yelling should be extremely rare, but anything involving death or getting maimed is a definite candidate.
You mention this happened on a sidewalk. Cars drive next to sidewalks. The American culture of cars is the number one cause of anxiety in my life as a parent to young children. I do not want to feel this anxiety, I do not like how it makes me react towards my children, who just want to play and have fun and explore the world and try to understand it. But cars exist. And today they are a much bigger problem than they were when I was their age, for a whole variety of reasons that are very well understood and articulated by people far more intelligent and capable than I am. And my children are, practically every single day, within 4-6 feet of cars that are a) much larger than they have any right to be, and b) driving much faster than they have any reason to, to the point that if they are careless about where they are, or what they are doing, they run a very serious risk of being killed.
That is why I sometimes respond to my children the way that I do, in line with what you've observed here. I don't like it, either, but it is what it is.
Now, I go out of my way to get my kids into big, wide, safe open spaces on a daily basis, and I will deliberately ignore them (within reason -- I keep tabs on where they are, etc.) so that they can go off and find interesting ways to play, hurt themselves, whatever. But I still have to engage with the automobile problem multiple times almost every single day of our lives.