Probably her, 1910
"United States Census, 1910," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MK4Y-1Y5 : accessed 22 July 2018), Gertrude Button in household of Mrs. Emma Button, Quincy Ward 2, Adams, Illinois, United States; citing enumeration district (ED) ED 35, sheet 9A, family 232, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 229; FHL microfilm 1,374,242.
Here she is in Denver in 1930, with daughter Emma:
"United States Census, 1930," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:X7W5-9P5 : accessed 22 July 2018), Gertrude Miller in household of Elmer Miller, Denver, Denver, Colorado, United States; citing enumeration district (ED) ED 34, sheet 19A, line 2, family 347, NARA microfilm publication T626 (Washington D.C.: National Archives and Records Administration, 2002), roll 233; FHL microfilm 2,339,968.
They lived in Englewood in 1920.
"United States Census, 1920," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MX2W-WTT : accessed 22 July 2018), Gertie M Miller in household of Elmer F Miller, Englewood, Arapahoe, Colorado, United States; citing ED 18, sheet 9A, line 27, family 235, NARA microfilm publication T625 (Washington D.C.: National Archives and Records Administration, 1992), roll 155; FHL microfilm 1,820,155.
Gertrude and Elmer, one child still at home in 1940:
"United States Census, 1940," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:VRDP-DSS : accessed 22 July 2018), Gertrude Miller in household of Elmer F Miller, Tract 10, Denver, Election District P, Denver, Colorado, United States; citing enumeration district (ED) 16-197, sheet 2B, line 50, family 36, 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 489.
Meet Elmer Franklin Miller, born 8 Oct 1881:
"United States World War I Draft Registration Cards, 1917-1918," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:KZKZ-G3V : 13 March 2018), Elmer Franklin Miller, 1917-1918; citing Arapahoe County, Colorado, United States, NARA microfilm publication M1509 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,544,477.
