Somehow she knows you recorded the conversation when you kept pushing at her regarding the doctor. She has brought this spying up too much and has almost pinpointed when you did it. I think she gave you a chance, both in the email and then face to face, to see if you would tell her.
Now, in this last conversation, she sounds like a woman who wanted to be free to take on some parental responsibility without you breathing down her throat. She didn't chose a good way of doing it, but that seem to be her intentions. She did not paint a very good picture of you. She made you sound very controlling.
Her reason for taking the child sounded very legit. I don't think she should have been so secretive about it and from what you had said, it sounded creepy to me. So now, her story is sounding better, but yours isn't doing so well. My question is why didn't you just tell her that it extremely upset you at the thought of your son going to some psychiatrist and her not willing to give any information. Instead, you tried to kiss her a$$! You've dug yourself into a hole.
My advice is that you call a DB Coach and get a professional to tell you what to do to. If you come clean about recording her, you're sunk. If you don't come clean, you're probably sunk anyway b/c I think she can read you well enough to know.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!