Thanks for your note. I did not have the name of Obadiah B.'s first wife, so that adds a useful bit. I presume that she was the mother of Claude, but not of the other children, based on their dates of birth.
I do not have a Margaret Louise Saunders and would be interested in learning where she fits in the Saunders tree. Another relative, Margaret Marshall Saunders, author of Beautiful Joe, also did some research on the family, and I have a photocopy of her typescript, which shows the same line, if I remember correctly.
Nether James Saunders (the earliest one you mention) nor his father John (who may not have come to America) was on the Mayflower, so it would be interesting to know what line she was claiming for that descent. It may have been through Catherine Rhodes, whose maternal grandfather Alden Bass, was supposed to have been named for his ancestor John Alden, but documenting all the steps to the satisfaction of the Mayflower Society might be difficult.
The Timothy Saunders, born 1751, that you show married to "Mary Neilly", was actually married to Martha Neily, as noted elsewhere in this thread.