You will not receive the level and depth of help you require on the internet.
You're doing the right thing, so far.
I suggest you discuss with your lawyer (or another lawyer) a "malicious prosecution" civil lawsuit or some other remedy available in your jurisdiction.
It might also be wise to make your child exchanges in a police station or sheriff's office.
Again, I suggest you speak with your lawyer about protecting your backside.
NY is a "one party" consent state, as far as recording the telephone calls with this family of evil doers.
I'd record every conversation I had with each of these creatures.
I'd also take a video recording of the child's appearance each and every time I picked her up and returned her to the evil mother!
The judge in your current custody matter might eventually sanction her for her frivolous false filings (I love alliteration)!!!!