Wow, I'm so very sorry you are going through this.

It was definitely NOT okay for your therapist to speak with anyone else in your family (or anyone in your life) without a signed consent from you. Furthermore, she breached confidentiality in a huge way by acknowledging (even if by default) that you are her client. This is a big no-no and kind of a basic tenet of therapist/client confidentiality.

You have every right to feel angry, sad, upset, and confused. I would feel the same way. I hope you give yourself lots of space and kindness as you work through this. Whether this rupture is reparable or not (which is only for you to decide), this will still have trust implications for you going forward with any therapist. This is a big deal. Don't let anyone tell you it is not.