OK so all of this is over what school your daughter goes to?
A church school will give her a better education than a regular public school. I see no reason to gripe about that.
The teachers make them toe the line and don't take any crap off the kids.
I live next door to a Catholic school and the kids are well behaved and get a great education.
I thought is was about your CDing.
If you are worried about her blabbing to others that you CD act like it doesn't bother you and that will take the wind out of her sails.
If someone asks you just laugh it off and say my ex drinks too much so no telling what she might say.
Don't let her blackmail you be a man and stand up to her.