Marcia, the 1880 census of Hickman County, Tennessee shows a William Rosson (vice Rawson) age 59 (born abt 1821)and a wife Elizabeth age 46 (born abt 1834)with following children John 18 Jeff 15 Amanda 11 William 9 (which would fit your birth date of Nov 4, 1871) Mary 3
None of the Elizabeth Aydelotts that I have in the Aydelott family of Hickman County match the age of this Elizabeth. Would you share your source that the maiden name of Elizabeth was Aydelott?
In a search of the census prior to 1880 I failed to find William and Elizabeth which may mean they came from outside Hickman County.
Finally, in Spence's History of Hickman County he list one William Rosson as a member of Company I, Tenth Tennessee Cavalry (Civil War) which included men from Hickman County along with those of Humpherys and other surrounding counties.