I remember having the same anxiety you have expressed. I went from being a bedside nurse to a clinical coordinator of a small 10 bed unit, to a nurse manager of 2 units in the same hospital. Then I moved many states away and took a chief nurse position for an 80 bed hospital. With each promotion, I remember having terrible dreams of my staff absolutely tearing me apart at our first staff meeting and had many fears about whether I knew enough to be responsible for all the policies and deciding what the standard of care should be, meeting the JCAHO standards, dealing with personnel problems, etc.
You may be taking a position in a system that is a political minefield, but don't let you self talk limit your potential. Obviously one person in senior management sees the potential in you. If that person is successful in the organization, latch on to them and learn from their years of experience. If you trust that person, they can usually help you navigate through the politics and teach you the unwritten rules in the organization (and believe me, every place has many unwritten rules).
If you do take it, I recommend assessing who in the organization is viewed as successful, who receives support from administration and the corporation, who gets things done, who comes back with a "YES" answer. Who has great people skills. Then associate with those people. Make some friends outside of nursing too (I have always made it a point to befriend the top HR person, plant operations too). Lastly, remember you are never alone in a healthcare facility. If you get into a situation where you don't know what to do, ask others who do know.
Before I started a new promotion, I always felt terrified inside so I would go out and buy a few new really professional looking outfits so my appearance would portray confidence even though I was anything but on the inside. What was the name of that movie starring Melanie Griffith, Harrison Ford and Sigourney Weaver? Working Girl?
As far as your family is concerned, that's a personal decision.
I say go for it. If it doesn't work out, it will teach you many things and if you have had many successful positions already, one risk is not going to derail your whole career. Thats just my 2 cents.