So if you are looking to become a manager I would encourage a MSN rather than just an MBA. An MSN/MBA is a good option though if you are considering moving up the ladder. MBA is quite common in director and executive level. My guess is the MSN you are looking at that is MSN/nurse leadership is not a dual degree program. It is probably an MSN with a focus on nursing leadership. Most programs are set up with MSN programs that have specific focuses whether that is in leadership, education, CNS, informatics...many options.
The school really doesn't matter unless you are going towards the Nurse Practitioner route which would require accreditation to take the NP exam. There is no required exam for non clinical MSN but an accredited program would be the preferred because its likely not a good program if its not accredited and the goal is the knowledge not the degree necessarily.
If you are going to continue on for a doctorate degree in nursing I would not encourage an MBA... unless you are going to pursue a PhD in business. it would be a waste of your time/money otherwise in my opinion. If you are looking at leadership I would encourage you to look at DNP programs that have a management focus. PhD is really a research degree which can be applied to management but DNP would really make more sense in my opinion.
It sounds like you have a lot of ambition and that is awesome!!! I would encourage you to do a little bit more investigating about what will help you most though before you spend a lot of money and time on the wrong degree.