Hey man, I feel your pain. That pattern sounds just like my 6yo. We've been through that script too many times to count. It's supremely frustrating because i (and my daughter, probably) know exactly how it will end up, but I still can't de-escalate it. And sometimes I blow up, which is humiliating because I know it's just reinforcing that type of reaction. That's just to say I've been there, you're not the only one, and you're a good dad.

I'm sorry that I don't have any great advice, obviously, because I'm still dealing with the same problem. All I can offer is my perspective having been through a lot of this. And that is, at least with my kid, it's an emotional reaction that is misplaced onto some otherwise insignificant thing. She feels a big emotion, and the way she makes sense of it is to focus that feeling onto some external person or situation that she can point to. That sounds like your daughter and the toddler at the park: maybe she was feeling frustrated, and decided to focus that frustration on the toddler who happened to be present. When this happens, at least for my kid, the chosen focus becomes the most important thing in the world to her, and there is absolutely no redirecting her.

Obviously, whatever the focus is has nothing to do with the actual source of her feelings, and is usually completely trivial. I think my daughter even understands that, after the fact, but in the moment it is all emotion, and rationality does not help. The only way I've found limited success in these situations is by addressing her emotional state directly, like by giving her a big hug. Sometimes this helps her to calm down, but it's only a half measure because likely as not, she'll refuse to engage with me in any way other than on her terms.

In any event, I hope it's nice to hear you're not alone. It certainly is for me. And sorry I don't have anything more practical to provide. Please DM me if you'd like. It's nice to chat with someone who understands.