The woman is. She is the HOA president, so what? It isn’t the responsibility of the HOA to control the behavior of neighborhood kids. She says that she was patrolling the neighborhood? That isn’t her job, either.
If she (or anyone else in the neighborhood) has a problem with the behavior of children, you go there as a neighbor and complain to the parent. What you don’t do is go there talking about how you are the HOA president and trying to use that as some sort of show of authority to throw your weight around. The guy answering the door is a lot more polite than I would have been in that case.
However, had an adult or adults come to my door and politely complained about the kids harassing them, I would have asked the kids to tone it down. It’s all about presentation.
That’s the main reason why I am on the board of my own HOA. I am there to make sure that some authoritarian asshole doesn’t become a little dictator. I do everything that I can to tell the neighbors that the HOA can’t do (x) or (y) because that isn’t within their power.
Yes, I know that many of you will say that you won’t live in an HOA community, but that just isn’t how things are here. Half of all homes in Florida, and 85% of homes built within the last 20 years, are in communities that are controlled by an HOA. I would disband our HOA in a heartbeat if I could, but that won’t happen, so I do the next best thing. I make sure that they don’t become tyrants.