Living well is your best revenge!
To me, Facebook is a spectator sport.
There really isn't any recourse for what your Ex posts on FB or says out loud. I would assume if she posts it on FB, she either says it or otherwise communicates her feelings to your children.
On the positive side, if you don't live down to the image your Ex conveys to your children, eventually they will figure out who is full of crap and who's opinions are trustworthy.
Consider it a challenge to be better than the lies people tell about you.
Be safe.