In the 1910 census your grandmother is listed as Annie C., but in 1900 she's listed as Ammy C.In 1900 her date of birth is listed as March 1896.
There's a TN death record for an Amy Crear DEAN b. 30-Mar-1895 in Macon Co, TN, died 11-Jan-1946 in Macon Co, TN.Last residence Difficult, TN. Parents were William Luster JENKINS and Mary Etta ROBINSON.Though she is listed as widowed on her death certificate, her spouse's name is listed as Cooper DEAN.
There's a marriage record for Cooper DEAN to Amy JENKINS on 14-Nov-1917 in Macon Co, TN
There's a death record for Cooper Selton DEAN b. 24-Oct-1899 in Smith, TN, d. 11-Feb-1942 in Macon, TN.Last residence Red Boiling Spring, TN.Parents were James DEAN and Jane YOUNGER.Spouse was Amy JENKINS.
The 1930 census for District 7, Macon, TN: DEAN, Cooper C. age 30 b. TN, both parents b. TN wife Amy C. age 33 b. TN, both parents b. TN dau Joulla age 11 dau Annis L. age 8 son James C. age 5
There's a death record for their daughter, Wyona, b. 24-Dec-1920, d. 14-Feb-1921.
In 1900 Cooper is listed as "Sulton C." He is living with his parents, same location as 1930, and siblings:Nettie, Alley, Pearly, Lessley, Ellis, and William.
In 1910 they are in the same location and he is listed as "Selton C."
In 1920, he and wife "Annie" are living with his parents and they have a 10 month old son, Joe E.
In each of the above censuses his mother is listed as Mary J., not Jane.