Livingston Clue Doesn't Work

I stopped at Clermont State Historic Site today and looked through the Livingston genealogy in the visitor center.  My Livingston clue did not fit into the published genealogy.

Here is a graphic representation of the relationships I found.  I think Catherine Livingston was related to Sarah Livingston.  Here are my reasons why.

• Catherine was born five years after Sarah, in Castleton that is not terribly distant from Ancram where my gggreat-grandmother Sarah Livingston was supposedly born, or Hillsdale where Sarah's mother Rachel was born.
• Catherine and Sarah both had a mother named Rachel.  Her father was listed as James, a common Livingston given name. Sarah's father was listed as Daniel, and I'm not sure that was correct.
• Catherine married Sarah's son-in-law's brother and ended up living in the same area, What brought Catherine to the area in the first place?  To visit Sarah?  

I have to find out more about James Livingston of the Castleton area.  I also want to see if I can find anything about Rachel Boyes' marriage to Lawrence Vosburgh.  He was her third husband. Possible branches Sarah may have come from is James Livingston in the same area as the patroon; Washington County, New York; or Wallingford, Connecticut.  From what I read on-line, those branches all go back to the same Livingston family in Scotland.