Impossible to be an armchair QB in this situation. There are so many different ways and levels that a parent can say "shut up" to a kid, and I can definitely see the extremes as a parent to a young child. I would tend to side with the psychiatrist as *in general* they're more trained to sense the nuance. That being said, current events are very hard on a lot of people, especially with remote learning starting for most families, so unless there was clear verbal abuse, I wouldn't have intervened.
Verbal abuse?? If l had a $ everytime a parent said ," when you get out of here l am giving you a butt wiping " or something like that, l would be a billionaire. Unless there is clear cut physical abuse, move on. Verbal abuse, like if the mom was saying" your a fat, lazy, ugly child, and l hate you" in public maybe. But even then, a law is not broken " shut up or something like that repeatedly to yell at a child is not her business, and can get you hurt by the wrong person.