Question regarding references after being fired

Hello, I am seeking some advice on how to proceed with my career. I graduated in 2007 with my BSN and was hired into a PICU. I didn't realize it at the time, but this unit had never hired a new grad before. I was assigned 4 different preceptors and had a very unorganized orientation where I was just kind of "cut loose" after a few months. Shorty after being off of orientation, I was fired for "not asking enough questions" and not performing at the level they had hoped I would be at after orientation. However, I left on good terms with my former director and manager knowing that they would still have to be references for me in the future.
I moved to another state a few months later and was hired as a home health nurse. I did well in my position and even won an award for nurse of the month. Well, boyfriend got transferred to another state for his job, so we recently moved again. I interviewed for a positition in a pediatric neurology clinic where I was interviewed directly by the program director. She called me the following day and gave me a tentative offer of employment pending my reference checks. Now, the HR department is holding out giving me a formal offer of employment because my references were "mixed." Is there anything else I can do to persuade them that despite my past firing I would be a good choice for this position?