How ignorant and blind she must be to see she has clearly become corrupted. I do have to say one thing to you Steve, If you can get a good lawyer, because chances are she'll probably try to pull the "you're a sexist" card in which a majority of juristicional systems will turn and see her as a victim.
The only thing I do see that could potentially bite you in the butt, though she did not directly say "don't send me any more E-mails" is the fact that she had mentioned you to stop. Nonetheless I am inclined to agree with you this woman (if you can call her that after her childish tendancies) does have something wrong with her. You ask me though near the end of your E-mails and her responses, sounds more like to me she was doing what little kids do when they're mad at their parents, Try to get the last word.
Personally, I think you're doing a fine job, as I didn't see anything threatening from you to her at all, much more the other way around "IE: I will call the police, I will do what I am good at and investigate your cyberbullying acts" Quiet frankly if defending yourself and counter posting to unreleveant petty assaults directed to you, is cyber bullying her, then I'm clearly the Queen of England, dressed as a sir with a tophat and monocle, I digress however.
It seems with this idiot's mass lunatic hate, and self rightous responses, she's the one who's turned this into a cyberbulling act, on a sidenote She is right about one thing, you were a bit aggressive in the sense that you ripped her a new one, I'd simply love to see her unrelevant responses and petty jabs at your personal life as you bring it up in court how she was the one to start firing upon you first.
If anything I'd say don't worry about her, keep a good head on your shoulders, print out the E-mails she wrote to you "if you haven't deleted them already" and highlight the comments she attacks you.