I get that you feel like you should have stood up for yourself but I think it could have gone far worse if you had done so, without first taking time to think it over, as you are actually doing.
My first thought was that you are dealing with someone who is mentally ill or suffering from an early stage of dementia. Of course I don't know that for sure but I think it's highly likely. So it never hurts to step back, and when you do react, try to do so calmly and kindly. You never know what's going on in her mind, for her to have such a strong, OTT reaction. Perhaps she is even frightened. Who knows, right?
How about something like this: "Oh, I'm sorry you don't like the noise. But you know, as far as I know, children are allowed to play outdoors in the afternoon, on public property. I'll definitely try to keep their noise to a minimum, though. Have a nice day, ma'am." If she keeps being unreasonable, just go on your way and try to avoid being near her home, as much as possible.
Also, some old bat flying out of her house all crazy, shrieking at little kids playing is a bit hysterical. Just another perspective. Good luck with it!