Several quick thoughts: it sounds to me, if I understand correctly, that people at your hospital are trying to set up an entirely independent union, not affiliated with any larger organization There are places with single-bargaining-unit unions that are fairly successful CRONA at Standord University Hospital being an example. But they are the exception. for the most part, a larger union with more power and more structure behind it will be more effective. But not always. In some places the absence of collective bargaining by state nurses associations has led a variety of non-nurse unions - Teamsters, Laborers, Steelworkers and others - into representing nurses. Not always too successfully. As a board member of a nurse union, I can tell you that the complexity of running a union - just in complying with reporting requirements and such - is immense. A big challenge for a new independent organization. I'd be leary of that idea.
And, in response to another comment further up: No state can prohibit nurses unions, at least in the private sector. Some states have so called "right to work" laws, which prohibit a contract that makes union membership mandatory for a particular workplace. In those states, unions tend to be small and weak and not common. But there are no states where unions are illegal - even though a lot of managers will lie about that and love for you to think they are illegal.