The Red River country cited is probably an area near the Kentucky/Tennessee border.
You need to find a copy of the following book which has a wonderful history of the Purviance family who came to America from Castle Fin, Ireland:
THE PURVIANCE FAMILY: A Genealogy With Allied Families by the late Stuart Hoyle Purviance Copyright 1986 Privately printed
Samuel's father, William Purviance "built an elegant home in Masonborough which was named Castle Finn after his home in Ireland."There is a good description of the house (no longer standing), ancestors, and descendants of your Samuel Dinsmore Purviance.
The above noted William Purviance was the son of son of Samuel Purviance and Lettice Dinsmore.Hope this helps.