I am not related -

The 1880 US Federal census finds William and Lucretia Elliott to be in Hawesville, Hancock county.

Based on your information of the great grandfather you know as Albert E he was listed as James Elliott age 9 and brother Eldred was 4. William Elliott is living with son Eldred in Utility 1900 census.

1880; Census Place: Hawesville, Hancock, Kentucky; Roll: T9_417; Family History Film: 1254417; Page: 196.4000; Enumeration District: 117; Image: 0397.
Wm. Elliott age 45 born KY 1835 father/mother reported KY
Lucretia Elliott age 38 born KY 1842 father/mother reported KY
Wm. Elliott age 16 son KY 1864
Eliza Elliott age 13 dtr KY 1867
James Elliott age 9 son KY 1871
Eldred Elliott age 4 son KY 1876
Martha Elliott age 1 dtr KY 1879

John Minnett 26 1854 OH parents Ireland
Elizabeth Minnett 25 1855 KY
Mary Minnett 6
Marten Minnett 5
Thomas Minnett 2
Mary Elliott 67 mother in law 1813 KY parents listed KY
Sallie Elliott 37 sister in law

1900; Census Place: Utility, Hancock, Kentucky; Roll: T623 524; Page: 11B; Enumeration District: 43.
Eldred Elliott age 24 born Dec 1875 KY married 3 yrs said farm property was mortgaged
Matlilda Elliott age 27 born May 1872 KY mother of 1 child
Eula May Elliott age 9.12 born Aug 1899
William Elliott age 65 father born Sept 1834 KY widowed

1910; Census Place: Utility, Hancock, Kentucky; Roll: T624_479; Page: 12A; Enumeration District: 61; Image: 179.
Eldael Elliott 35
Tilda Elliott 37
Elah Mary 10
Charles 8
Oscar 1 yr 6 mos died 2 July 1911

1920, Hawesville, Hancock
Allen E Elliott 1871
Maggie 1877
Gilbert 1902
Thomas 1906
Fielden 1909
Brooks 1918

1920;Census Place: Pellville, Hancock, Kentucky; Roll: T625_573; Page: 10A; Enumeration District: 67; Image: 574.
Eldred E Elvert 45
Matilda Elvert 47
Charlie E Elvert 18

1930; Census Place: Pellville, Hancock, Kentucky; Roll: 745; Page: 7A; Enumeration District: 10; Image: 1146.0.
Eldured J Elliot 54
Matilda Elliot 56

1930; Census Place: Corbin, Whitley, Kentucky; Roll: 781; Page: 19A; Enumeration District: 11; Image: 778.0.
Charles E Elliot 27
Mary E Powell Elliott 29
Thomas C 5 born 28 Jul 1924 Whitley Co
Chistden L 3 - Chrestine L born 28 May 1926 Whitley [Christine]

1930; Census Place: Louisville, Jefferson, Kentucky; Roll: 758; Page: 2A; Enumeration District: 151; Image: 1028.0.
Charles Elliott 28
Elsie M 24

1930; Census Place: Marked Tree, Poinsett, Arkansas; Roll: 88; Page: 18B; Enumeration District: 7; Image: 795.0.
Chas Elliott 29 KY
Sadie 25

WW I Draft registration cards, 1917 - 1918
Name: Eldrid J Elliott
City: Not Stated
County: Hancock
State: Kentucky
Birth Date: 17 Dec 1875
Race: White
Roll: 1653475
DraftBoard: 0

Source Information: Ancestry.com. Kentucky Death Records, 1852-1953 [database on-line]. Provo, UT, USA: The Generations Network, Inc., 2007. Original data:
Kentucky. Kentucky Birth, Marriage and Death Records – Microfilm (1852-1910). Microfilm rolls #994027-994058. Kentucky Department for Libraries and Archives, Frankfort, Kentucky.
Kentucky. Birth and Death Records: Covington, Lexington, Lousivlle, and Newport – Microfilm (before 1911). Microfilm rolls #7007125-7007131, 7011804-7011813, 7012974-7013570, 7015456-7015462. Kentucky Department for Libraries and Archives, Frankfort, Kentucky.
Kentucky. Vital Statistics Original Death Certificates – Microfilm (1911-1955). Microfilm rolls #7016130-7041803. Kentucky Department for Libraries and Archives, Frankfort, Kentucky.

Name: Matilda A Elliott
[Matilda A Allgood]
Death Date: 2 Aug 1948
Death Location: Jefferson
Residence Location: Jefferson
Age: 75
Gender: Female
Ethnicity: White
Birth Date: 17 May 1873
Birth Location: Kentucky
Spouse's Name: Eldred J Elliott
Father's Name: David Allgood
Father's Birth Location: Kentucky
Mother's Name: Mary Catherine Bowlds
Mother's Birth Location: Kentucky

Name: Charles E Elliott
Death Date: 25 Dec 1973
Death Place: Jefferson
Age: 072
Residence: Jefferson
Volume: 64
Certificate: 31707

Name: Oscar Elliott
Death Date: 2 Jul 1911
Death Location: Hancock
Residence Location: Hancock
Age: 2
Gender: Male
Ethnicity: White
Birth Date: 5 Dec 1908
Birth Location: Hancock
Father's Name: Eldred Elliott
Father's Birth Location: Hancock
Mother's Name: Matilda Algood
Mother's Birth Location: Daviess

Name: Otto Levi Elliott
Death Date: 28 Sep 1912
Death Location: Hancock
Residence Location: Hancock
Age: 0
Gender: Male
Ethnicity: White
Birth Date: 28 Sep 1912
Birth Location: Utilily, Kentucky
Father's Name: Eldred Elliott
Father's Birth Location: Utility, Kentucky
Mother's Name: Matilda Algood
Mother's Birth Location: Daviess

Name: Elizabeth B Elliott
Date of Birth: 12 Jun 1917
County: Hancock
Mother's Name: Margerett Arnold
Volume Number: 60
Certificate Number: 29843
Volume Year: 1917