(As a union shop steward for years), I would say do not run to a manager. Too often, I have had managers go after the totally justified complaining nurse and not the true problem child.
If at all possible, try to deal with it one on one. Having a supportive co-worker during these difficult conversations is not a bad idea. Often waiting until things cool down is helpful.
I have gone into work places were there are ongoing issues, usually with one repeating toxic nurse. I have had toxic nurse seek counseling, use EAP for assistance. I have made sure they have had due process during their ongoing disciplinary hearings. It is an awkward position to be in. I will take the offending nurse aside and explain, I am not defending your bad behavior, I am only making sure the proper disciplinary process is being followed. Also, known as "how the cow ate the cabbage conversation."
I almost always saw these issues come up during the probationary period and management did nothing. Too often management looked the other way for years. It is a nightmare, for the entire workplace.