Litigation for breach of teacher/student confidentiality?

Practically speaking, I would have a meeting with the principal to discuss your concerns and have the school resolve the matter internally. A lawsuit would likely end in the same result: disciplinary action.

I strongly agree with Attorney Anderson. You would not want to sustain an actual lawsuit unless the breach of your son's confidential information becomes systemic--meaning, more than just your son's teacher, but supervisory persons in school administration are a part of compromising your son's well being or confidentiality. Based on the facts you described, the best approach would be to seek a reprimand through the proper administrative channels. Should doing so prove ineffectual, reach out to a licensed New York attorney who regularly practices public education law. This attorney could bring pressure to bear upon the school district in which your son is enrolled. I wish both you and your son the very best.

You can't get her fired. You can - and should - write her an email stating that you are concerned that she has discussed your son with other parents and that this violates your right to privacy and your son's right to privacy under federal law - and that you hope she will respect your privacy in the future. If the behavior continues, send that email again, but with a copy to the principal and ask for a meeting to discuss this.

I do not think that there is enough here to warrant you commencing a lawsuit against the teacher. As you have been advised by my colleagues, it may be best to speak with the school principal and the teacher about this situation to resolve this in an amicable manner. A lawsuit will take too long to resolve, which may just end with the teacher receiving disciplinary warning.