I am really leaning towards this person. Bertha Johanna Wacker. She lived in Denhoff, ND in 1910. She never married. 1920 and 1930 with her siblings in Montana. I don't know if you are familiar with Germans from Russia but that is the group her family belonged to. Wacker and Walker could easily have sounded the same with the pronunciation with this group. If you can find an older family member of this family they may have known something. Although, it is always possible it was never talked about.
I can't get into the census records for some reason tonight BUT the part I can see it does list Bertha Wacker in 1910. 1920 she is listed (as is the family) as Bertha Walker. 1930 as Bertha Wacker.
1900 in Township 97, Hutchinson, South Dakota
1910 Wacker in Denhoff, Sheridan, North Dakota
1920 Walker(Wacker) in Missoula, Missoula, Montana
1930 Wacker in Great Falls, Cascade, Montana
In 1910 it does put both Bertha Johanna and Emery in North Dakota.
I also see your grandmother's birth middle name is the same as Bertha Johanna's mother's first name. Check out the census records.
South Dakota Birth Record:
Name: Bertha Johanna Wacker
Birth Date: 14 May 1886
County: Bon Homme
Father's Name: Johann Wacker
Mother's name: Katherina Jasmann
File Date: 16 Feb 1942
Name: Bertha Wacker
Estimated Birth Year: abt 1886
Death Date: 21 Nov 1948
Index Number: GF 11834
Source: Montana Office of Vital Statisticshttp://www.montanagenweb.com/Cemetery/waataja-weymouth.html
WACKER Bertha J. 21 Nov 1948 Great Falls MT New Highland Cemetery
There is also a headstone photo for Bertha Johanna on findagrave.com
Mother's death record:
Name: Katherine Wacker
Estimated Birth Year: abt 1856
Death Date: 24 Aug 1935
Index Number: GF 5803
Source: Montana Office of Vital Statistics
I am curious how you knew the parents names.