It sounds to me like that person you met in the park may have been mentally ill. It is not normal to be that aggressive without provocation.
I have not enjoyed reading how people have been gleefully saying what they would do to her. Maybe her life is constant suffering because she suffers from paranoid delusions or something. Maybe she has no health insurance and cannot get treatment.
Apart from that, if you do find someone who is very agressive like that, taking them on is not a very wise thing to do. If she is in a place where she finds attacking a child to be OK, how do you think she is going to react to you attacking her? It was lucky the policeman was nearby. I wonder if he requested a psych consult for her while he had her in custody.