I'm not saying you were wrong at all...in fact, I think you are totally "in the right." But - does the chain of command start with speaking directly to the person you're having the problem with, and then going to the supervisor if/when that fails? (I'm genuinely asking
Even if you technically
should have started by talking to Charge Nurse directly, I can certainly see why you didn't! "Freaky" seems to be an understatement (?).
I am baffled as to how Charge Nurse gets to be Charge Nurse when she acts so childish...and I am baffled as to why should would bring your family into it at all? Weird. Does she know your family and/or do her kids go to school with your kids? If so, I would definitely take her comments as a threat and would go up EVERY STEP of the chain of command (including the DON and the HR dept.) until I found someone willing to address this issue with Charge Nurse. (She should be severely reprimanded for her statements and retaliatory actions.)
You are right on the money turning in this writeup to the DON, in my opinion.
BTW, I also think you handled it very well and very professionally when she brought your family into it. This was a great response:
I told her once again that my family has nothing to do with this situation and that I thought the conversation was taking an extremely unprofessional and threatening turn on her part and that I didn't care to discuss it any longer.
Good job! You kept a "cool head" and said exactly what you should have said here. Called her on it and set the boundaries!