Sue, first of all, congrats on getting the offer
Here's my two cents worth. The key question is what you REALLY want to do career-wise. This promotion would definitely be a step into management and away from direct care - neither good nor bad in and of itself. However, if direct care is what you definitely want to do then this might not be for you.
Pros:
A chance to take on more responsibility and grow to the next level, especially if it leads you somewhere you've been hoping/striving to go.
Cons:
Less day-to-day patient care/interaction and responsibility for managing the team.
Not everyone is cut out to be a manager and it is a wise person who recognizes that about themselves. That said, your icky experience at the other NH is not necessarily indicative for the reasons you stated - they definitely didn't give you the tools to succeed.
It can be hard but look at where you really want to go. Me, I loved to get to the next level and have my fingers in more pies

but DH was offered a promotion and choose to stay where he was because he prefers hands-on so it is all about what is right for you.
Now, after all the cautionary stuff a promotion is super and you will grow into/with the job and make it take on your personality and you will keep your patient contact because it is important to you, especially if you have a supportive management team above/beside you, which it sounds like you do.
Good luck either way!