When I was first reading your post I was asking myself, "I wonder if you've made it clear that what she is doing is ridiculous?"
I guess the way (if you're interested in furthering the relationship) is to NOT talk online, but on the phone and just give her a, "Here's the deal. This is really bothering me, and I want you to hear me out." The first thing I would do is make sure she knows that what she's doing by video taping / snapping photos is in some places absolutely illegal, but also exceptionally rude. Everybody has the expectation of privacy when they're in the hospital, and *I* have the expectation of not having people come find me at my house after taking care of their loved ones. Posing the question, "If you were at work, would you find it appropriate for people to snap photos of YOUR name badge?"
The ultimate finale to your conversation is this: If she refuses to listen to reason, refuses to change her way, and YOU find it unacceptable and not good for your mental health (I wouldn't think it would be), then I would definitely tell her, "I'm sorry, I understand you have health problems, but from what I can see you're trying to blame somebody else for your issues. You need to realize these are people that are trying to help you, and the only reason you're getting the impression that they're being jerks is solely because you're being an a**hole to them first. Very few people are in the nursing or medical profession for reasons other than wanting to help others get better and further their lives. Until you can realize and accept this, and stop being such a horrible person every time you're admitted to the hospital, for my mental health I'm not able to be friends with you. You are the exact reason why some days healthcare professionals have a horrible day at work. If it wasn't for people like you and you're disparaging attitudes towards others and having the mental image that we're there to attempt to hurt you on a daily basis while admitted, then our jobs would be so much more enjoyable. Please revisit your attitude, check it at the door when you get admitted, and maybe realize that being a bit more humble and less of a bi**h is a nice quality to have. Until that time, though, I don't really think I have anything in common with you anymore. I'm sorry that God gave you an illness that you are disabled from, however had you not had treatment from this disease, you would probably be dead right now. If you are thinking this is a proper and amazing alternative to the way you live your life right now, then make yourself a DNR-CC or DNR-CCA and leave it at that, and leave it in God's hands."
Alternatively you can ask her to see a psychologist, however I highly doubt she will.
I'd never EVER be able to tolerate that. And when I'm confronted by MY friends that DO have disparaging comments about healthcare, I fully listen to their complaints, and then give them both sides to what COULD have been happening. If they refuse to listen to it, I change the subject and move on.
Finally, you don't need toxicity in your life. Cut that complaining jerk out of yours. You have to deal with enough of that s**t at work yourself.