You say you want to work with this producer again. Well, depending on how much you really want that contract, you can be proactive. Yes, ownership of a show is a delicate subject, and everyone I know has been called on the "my show" word use at one point or another. So if you can be truly dispassionate and/or feel truly appreciative (who says SMs can't act), find a way to deliberately thank that producer - tell her simply and clearly (without elaborating) that you learned from her note, maybe even mentioning some of the thoughts raised on this board (altho, don't mention throwing it our way). If you can do this very very simply, with as much truth as possible and with a humble spirit, you will gain an ally. And it sounds like you need her to feel like your ally to get anything done.
On the other hand, your description of her as someone who stops rehearsal to put in her two cents, who gives notes directly to performers and designers rather than through the director, who berates you in public, who doesn't listen when you pass along notes from the directors etc., well, she is clearly someone with power trip issues and without any practical skill sets for theater. If she is so needy, so desperate to be the center of attention and as such has no concept of theater protocol, you have no way to win here. Therefore, you may want to rethink your desire to continue with this company. If you have tried to explain nicely, stood up to her professionally, or had someone she actually listens to explain about lines of communication and how rehearsals are run and she still acts this way, why would you want to stay and put up with her disruptive and destructive behavior? Just cuz she is a producer? You can let those you respect know that you would love to work with them in future (again, without elaborating...don't shoot yourself in the foot and get branded as a complainer) but start looking for your next gig without waiting for this show to close. That way, you do the honorable thing and stay till it's done, but you will be prepared to move on and not wait for them to decide your fate for you.
and, well, good luck