RAI- Take comfort in the fact that if they are resorting to cheap threats - they must not have anything more meaningful to work with.
Are these communications going to your lawyer first - or are they sending them directly to you? If they are not doing so already - have them send all correspondence to your lawyer - that will spare you some of this.
For what it's worth - it doesn't sound like there is anything new here. It sounds to me like she is seeking out a lawyer who tells her what she wants to hear. That's probably good for you.
Shake it off as best as you can (easier said than done) and get back to focusing on work and the kids.