How did Kate Bradley come to run the Shady Rest Hotel?

Many Sit Coms have a missing parent that we never really know of their demise +-

or at least I don't LOL

I think (after Kate 'went visiting' and never returned), Uncle Joe mentioned about the Bradley Sisters' great-grandfather having established the hotel way back when. I guess Kate's late husband had inherited it from his grandfather when Kate first met him then they ran it together during their marriage but since the girls were all still minors when Mr. Bradley died, Kate either outrightly inherited it directly from her late husband OR was given dower rights to it as the girls' guardian until Billie Jo (the eldest) came of age. However; it's interesting that NONE of the girls ever seemed to express an interest in actually gaining ownership of it even after Kate's . ..departure!