If the therapist thinks the client is in danger of harming herself, she is supposed to inform the parents. I'm not sure email was the best way to do that, but at least she tried. You wrote that your T had emailed your mom a different time too. Was this also about your being in danger? If not, it might be a breach of confidentiality. But my guess is your T was trying to protect you and make sure your parents knew you might harm yourself so they could keep a close watch on you. I think it would be good to clarify with your T what types of things she will share with your parents and what things will be confidential.

Does your Mom know and is she OK with your having her email password and checking her email box and reading her messages? If not, I think you should tell your Mom you still know the password so that she can change it. Even if she does know and is OK with it, I tend to think it is a bad idea...