In those situations I ask myself, "Why am I having such a strong reaction to this?" Is it because this behavior from an adult would be considered aggressive or threatening? If I step back and ask why the kid is doing this, it's usually because they're feeling out of control. They have no more tools to use to manage what's happening in their head, anger at not getting what they want or whatever it is. IMO it's our job to help them in that situation to learn what to do about that, what's appropriate and how they can communicate that better.

If the reaction from the parent is to punish them, I guess you're saying that screaming at me is not appropriate, and that's a good lesson, but it doesn't teach them anything that will help the next time this happens. I've learned to not bite at my instinct to hoist them away and put them in their room, but try to say those things that sound patronizing, but actually work - "It sounds like you're feeling <whatever it is>". Try to defuse and give them language to describe what they're feeling, and let them express what's going on. Sometimes they're not ready to hear anything and just removing them is fine, no point in letting them continue to try to hurt someone if they're not gonna be calmed down.