I think it would be more useful to set up a meeting with the person in charge of human resources who deals with training and licensing as regards HIPPA and privacy generally. Those are the people that educate the staff about the basics of the laws. Usually, they have to update these yearly (I think) and that person/training staff would be in a position to spread the message about this confidentiality issue with the staff and perhaps work in some new safeguards for the patients and families.
I think you have a great idea and I think the doctor deserves a great big thank you and yes, an acknowledgement that you were in a bad place and your appreciation for helping your son and your family when you may have been a family that kept them up at night (and you likely were, according to my oncology doctors).