I have done extensive research on these families in Bedford; the likelihood that you will find documents there stating their parents is slim to none. Andrew Sheets does appear on the tax lists there, as does George and Solomon Sigafoos. Solomon may be Lydia's brother, and George may be her father, but there are other documents in Ohio that would suggest otherwise.
There was a second Andrew Sheets in Bedford who can easily be confused with our Andrew.
How are you related? Andrew Sheets and Lydia Sigafoos are my 3rd great-grandparents; I am descended from their son Samuel.