I work for a large insurance company with very extensive diversity training. I also deal with litigated civil cases and have seen some dealing with various elements of this type of case.
I'm not divulging any type of secret but a key element of these sort of cases is that the harassee has to ask the harasser to stop so I would recommend that you bluntly tell her to do so, ideally in front of a witness. If she does it again, you will likely covered that element of a case.
You may also be able to work in defamatory elements (saying or writing things which were untrue about someone...) which might be some icing on the cake (ha) as it were. I'm not an attorney so I may be blowing smoke a bit but I would do those things immediately and, if she doesn't adhere to your civil request, you can decide if you want to bear it or if you want to take a stronger stand, either through the HR department or on your own. You can choose not to but to protect yourself, tell her to knock it off.
Actually, the supervisor being involved and being a nurse, who should be expected to know more than the average "civilian" about diabetes, might add substance to your claim. I don't really want to talk about how these cases can be fought but a quick second look at your story makes me think you could build their behavior into an interesting case. If anyone who knows what they are talking about, i.e. an HR rep, got wind of such behavior, they would probably be very alarmed by it.