I checked the Binford Genealogy for information on the Binfords that you have listed.
I have found a "Peter Binford" born Sept. 25, 1822.He was the son of Josuah Binford born Jan 3, 1779/died Jan 6, 1844, and Lydia Patterson born March 2, 1778/died August 19, 1843.
Josuah is the son of James Binford and Hannah Crew.James was born in Charles City Co., Va.They located to Greensville Co., Va, when they married and in 1800 moved to Northampton, Co., North Carolina (where Peter was born).James died in 1824.
In 1826 - the entire family of James Binford and Hannah Crew moved to Rush and Hancock Co., IN.
This is how your Peter came to live in Hancock County.
Josuah had was the eldest of James and Hannah's children.There were seven total:Joshua; Andrew; Micajah; Angelina; James L.; Benajah; and Rebecca.
Joshua and Lydia also had a large family.There were nine total including Peter:Mason; Ashbel; Hannah; Mary; Joshua; Lydia; James; Peter; and Sarah.
The Binford genealogy also says that Peter Binford married Elizabeth Adams on August 22, 1844.Elizabeth was born December 8, 1829.They lived on "south banks of Blue River.
They had only one child:Sarah Jane Binford, born:Sept. 7, 1849 married April 10, 1873 to John McCorkle born December 8, 1850.
*I do not find a "Woodford H Binford," "Lily Lindsay;" "Charles T Binford" or "Clarence Binford" in the Binford genealogy.
I would believe that Woodford - must be from a different branch - that is not listed in the genealogy.
Sarah Jane Binford and John McCorkle had eight children:Louis T; Armilda; Lydia; John W.; Benjamin P.; Jmes E.; Franklin Bodine; and Samuel.