I think that people usually sue surgeon, hospital, nurses, anybody and everybody from whom they think they can get anything. It really depends on what evidence they have against which parties, on how aggressive their lawyer is, how angry they are and at whom, I would think.
I hope it turns out well for the innocent. If the nurses tried to tell the surgeon that something was wrong, if their pleas to him were ignored, minimized, or mishandled, if the nurses went up their chain of command and/or to the surgeon's Chief of staff/department, if you guys involved managers, supervisors, and did everything you could to rectify the problem, and if you documented your efforts and the fact that you did all you could, you might be alright. But who really knows? Maybe you want to talk with a couple of attorneys yourself to find out what they think.