If I were her, I could NOT stay out of this. Yes, family comes first, but she also knows the call of duty, and having let the cat out of the bag in this offhand way, all that’s left is to make it formal.
She doesn’t need to declare that she’s running for anything. Just come out and cut the ties with the RNC officially, and make a statement to the effect that “Unless the GOP is going to return to it’s roots and support traditional conservative values, we have no choice than to organize a new Party”.
When the buzz dies down (in about a week), take stock and see what public support looks like. I think that as soon as a viable alternative comes into existence, you will be amazed at the support it receives.
As I have said before, I will raise a million dollars for any campaign or movement she gets into.