So, this happened a couple of days ago but I'm still haunted by it. I took my kids to the park (7yo girl and 3yo boy) with some friends around the same age. Weather is nice so the park is quite crowded with kids and parents.

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As I'm talking with another adult, I see two boys (brothers, around 4-6) using sticks as guns and messing with my daughter. I decide to observe and see my daughter walking backwards trying to keep the distance with the boys (who keep getting closer pointing her with the sticks), while my girl is very timidly saying "stop". Since it doesn't look like she can control the situation I decide to get closer and say "that is enough" while I let my daughter "escape".

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Seems that the boys forgot about her so they come with their mom, which is sitting in a bench next to the adult I was chatting with (let's call him F) when this started. The boys keep saying that they're the police and that everybody else are thieves, pointing with the sticks and so on, whatever. F decides to take part into the role-play and says that he's the sheriff and try to convince them to play less aggressively. Doesn't work and before F realises the boys are poking him with the sticks and even jumping on top of him. The mom manages to snatch them away for a few seconds as I'm starting to see that this is not going to end well (the mom just smiled and said "oh, boys... you know").

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Suddenly I see both boys are doing the same to my 3yo, I walk calmly giving some time for my son to react but before I can separate them as I did with my daughter, one of the boys pokes my son in the temple. I honestly lost my shit, grabbed the stick and violently threw it away, which obviously caused the kid to start crying. Next thing I know is the mom yelling at me like crazy about what the hell am I doing and that they're just kids and I'm an adult. Still in adrenaline-rush mode I yell back that it was dangerous, they could've hurt my son's eye, etc.

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Then is when things go surreal. The mom starts to say that I hit her kid and that she was calling the cops. I was shocked and could barely say that I grabbed the stick and that's it. Luckily for me other parents (most of them I didn't know) jumped and started to say that it was false and that in fact those kids had been all evening harassing their own kids. The mom doesn't reason and keeps yelling and insulting me. This goes for a good 10-15min and then she starts saying that my daughter started everything  by bossing her two kids (the mom was imitating some sort of club-bouncer posse). We feel that she's delusional and that there's no way to reason so we took our kids away and went for ice cream.

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I feel bad for reacting in such a childish way, and honestly I was shaking for quite a while. I feel like most of the other parents in the playground were also upset with these kids but were nice enough not to cross the line. AITA?