this puzzler has been solved!
Mary's parents are William Cook (abt 1820 - before 1870) and Vesta/Vashti Canady (born 1819). She shows up with them on the 1850 census living in Barnwell County. By 1860 she was married to James Reed.
Mary and James Reed named their first son John William Cook Reed after both of his grandfathers. John was for John Reed, son of Samuel and Mary. William Cook was for Mary's father.
Mary's mother is found as Vashti early on, but was more consistently Vesta or Vesti later on. Mary and James named a daughter "Vesta Ida" who was listed as "Vesta I." on the 1870 census. She was most often known as Ida. Ida's son Samuel Reed Copeland named one of his daughters Ida Vesta Copeland.
William Cook's parents were Jacob Cook (1780-1861) and Eliza (born abt 1790). Vesta Canady's parents were John Canady (1780-1861) and Mary Johnson. Mary was born about 1800 and died after 1880. On the 1880 census, she shows up along with Vesta living with the family of Vesta's youngest daughter Ella in Rocky Springs, Aiken County, SC.
A portion of my brick wall still exists. I have yet to determine when Mary Cook Reed died or where she is buried. Also, her birthdate is still a quandary. The 1850 census has about 1839, 1860 census has 1840, 1870 says 1845, 1880 claims 1840, and 1900 has Feb 1844. I am going to use "abt 1840" until I learn something more definite.