"The kids are completely oblivous to any of our discussions."
They really aren't. She threw the stuff out the car window in the parking lot, in front of other people? The kids know that the halves that made them are now at war, and it is very hard on them, wether they show you that or not.
I wouldn't be afraid of her, I would just ignore her completely. She will never, ever, see your side of things or point of view. I had to keep telling myself, "You can't make sense of non-sense."