Kate's death record gives her mother's name as Frances Tankersley.
From 1900 US Census, Bethlehem, Chambers Co., AL:
"Lestura Gibson Head M 58 Georgia,
Elizabeth Gibson Wife F 51 Georgia,
Orrie L Gibson Daughter F 29 Alabama,
Warner Gibson Son M 19 Alabama,
Kate Gibson Daughter F 17 Alabama,
Inez Gibson Daughter F 15 Alabama,
Allie Chappell Boarder F 24 Alabama,
Sallie Jennings Boarder F 18 Georgia"
Kate married Charles Marshall Reeves on 1-6-1907 in Langdale, Chambers Co., AL.
From 1910 US Census, Langdale, Chambers Co., AL:
"Charlie Reeves Head M 32 Georgia,
Kate Reeves Wife F 24 Alabama,
Lottie Reeves Daughter F 12 Alabama,
Elizabeth Reeves Daughter F 2 Alabama"
From 1920 US Census, Langdale, Chambers Co., AL:
"Charles M Reeves Head M 42 Georgia,
Kate Reeves Wife F 35 Alabama,
Elizabeth Reeves Daughter F 11 Alabama,
Annie Lois Reeves Daughter F 9 Alabama,
Charles Reeves Son M 7 Alabama"
From 1930 US Census, Chambers Co., AL:
"Charles Reeves Head M 50 Georgia,
Kate Reeves Wife F 45 Alabama,
Charles Reeves Jr. Son M 17 Alabama,
Tinie Reeves Sister-in-law F 13 Alabama"
From 1940 US Census, Chambers Co., AL:
"C M Reeves Head M 63 Georgia,
Kate Reeves Wife F 55 Alabama,
Inez Gipson Sister-in-law F 52 Alabama"
Sources
"United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M9Z1-R31 : accessed 29 September 2017), Elizabeth Gibson in household of Lestura Gibson, Precinct 13 Bethlehem (east part), Chambers, Alabama, United States; citing enumeration district (ED) 16, sheet 8B, family 141, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,240,006.
"Alabama County Marriages, 1809-1950," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QKZ3-4ZTD : 21 July 2015), Charles M. Reaves and Katie Gibson, 06 Jan 1907; citing Langdale, Chambers, Alabama, United States, county courthouses, Alabama; FHL microfilm 1,290,839.
United States Census, 1910," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MK3Y-D2X : accessed 6 October 2017), Kate Reeves in household of Charlie Reeves, Langdale, Shawmut and River View, Chambers, Alabama, United States; citing enumeration district (ED) ED 35, sheet 13A, family 255, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 5; FHL microfilm 1,374,018.
"United States Census, 1920," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MXCL-H4S : accessed 6 October 2017), Kate Reeves in household of Charles M Reeves, Langdale, Chambers, Alabama, United States; citing ED 35, sheet 1A, line 55, family 2, NARA microfilm publication T625 (Washington D.C.: National Archives and Records Administration, 1992), roll 2; FHL microfilm 1,820,002
"United States Census, 1930," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:3D1Q-Z3Z : accessed 6 October 2017), Kate Reeves in household of Charles Reeves, Precinct 13, Chambers, Alabama, United States; citing enumeration district (ED) ED 29, sheet 14A, line 25, family 257, NARA microfilm publication T626 (Washington D.C.: National Archives and Records Administration, 2002), roll 3; FHL microfilm 2,339,738.
"United States Census, 1940," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:V1LX-8CD : accessed 6 October 2017), Kate Reeves in household of C M Reeves, Election Precinct 13, Chambers, Alabama, United States; citing enumeration district (ED) 9-32, sheet 5A, line 39, family 83, Sixteenth Census of the United States, 1940, NARA digital publication T627. Records of the Bureau of the Census, 1790 - 2007, RG 29. Washington, D.C.: National Archives and Records Administration, 2012, roll 10.
"Alabama Deaths, 1908-1974," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:JN8K-BYQ : 27 November 2014), Kate Gibson Reeves, 17 Dec 1970; citing reference 29934, Department of Health, Montgomery; FHL microfilm 2,033,363.
"North Carolina Deaths, 1931-1994," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:FG5N-3L3 : 17 July 2017), Charles M. Reeves in entry for Charles Marshall Reeves, 02 Aug 1977; citing Charlotte, Mecklenburg, North Carolina, v 29B cn 29669, State Department of Archives and History, Raleigh; FHL microfilm 1,984,316.
For daughter:
"United States, GenealogyBank Obituaries, 1980-2014," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QKWJ-HWBK : 15 September 2016), Charlie Reeves in entry for Mrs Elizabeth Reeves Hodges, Georgia, United States, 15 Dec 1994; from "Recent Newspaper Obituaries (1977 - Today)," database, GenealogyBank.com (http://www.genealogybank.com : 2014); citing Columbus Ledger-Enquirer, born-digital text.
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