References

I think your confusing personal references and employment history.

Your personal references are just that. People that you know and have worked with, and can speak to your character and work habits.  These are individuals that you choose, and may or may not be from your last place of employment.

Listing your employment history is where this gets complicated if you don't want to list your most recent employer.  Every place I have ever applied to has required a listing of all employment over a specified time, most commonly the past 10 years.  Leaving this employer off is going to create two problems.  First, this is going to significantly increase an employment gap on your work history.  Second, and potentially more significant, if you leave it off and are found out this would likely lead to termination forn falsifying your application.

If it were me, I would include it on the application and provide the number for Han resources.  Best wishes.

I think you can put down a charge nurse as a reference if you don't want to put the manager.

Depending on the area floor nursing positions are relatively easy to get.  You will have to have some personal and professional references though but they don't have to be your managers.  

When I was applying at another hospital where several people that I used to work with worked I contacted a couple of them and asked if I could use them as a reference, along with my best friend and asked them not to contact my current manager.  Ultimately I withdrew my application and changed my mind so I'm not sure how it would have worked out but in a facility that is short staffed and needing nurses, I'm sure I would have gotten the job easily without using my manager.

It still might be important for you to give your history of working there to show you have experience.