After further research yesterday ...
The family of John Mlinaric/Minarich and Mary Krazovich/Krznarich arrived in Menominee County, Michigan, between 1908 and 1910, and were in Whiting, Lake County, Indiana, by 1913, when daughter Celia was born.
Here they are in 1910, before Nick and Celia was born. The oldest son, John, was the husband of Helen Groarke. Evano is with John and Helen in 1930.
1910 Census, Meyer, Menominee County, Michigan
April 27, 1910
[indexed as Mauch. name looks like Mlrich with a few unreadable letters above the "l"]
John Mlrich, 39, married 1x, for 10 years, born in Austria (Croatian), parents also, arrived 1890, naturalized, speaks English, laborer, lumber mill
Mary Mlrich, 30, married 1x, for 10 years, 6 children, 5 alive, born in Austria (Croatian), parents also, arrived 1898, speaks Croatian
John Mlrich, 8, born in Pennsylvania
Joseph Mlrich, 7, born in Pennsylvania
Rosa Mlrich, 3, born in Pennsylvania
Evano Mlrich, 1, born in Pennsylvania
Stephen Mlrich, 2m, born in Michigan
https://familysearch.org/ark:/61903/1:1:MLR8-DQV------------
John Minarich/Mlinaric's death in Indiana in 1915:
Indiana Death Certificates
April 24, 1915
John Mlinarich
address 401 Stuber, Whiting, Lake County
married, age 48, a laborer
born in Harvatia/Horvatia, Austria
father: Matej Mlinarich, same birthplace
mother: Marey Karbich, same birthplace
informant: Marey Mlinarich, Whiting
cause: typhoid fever
buried: St John's Cemetery, Hammond, Indiana, April 26, 1915
[I found it on ancestry, it might be on familysearch, I didn't look]
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1920 John's wife Mary Krazovich/Krznarich with her second husband, and some children, including John and Celia:
1920 Census, Whiting, Indiana
January 5, 1920
at 312 119th Street
Bob Paradzina, 33, arrived 1913, papers pending, born in Austria (Croatian), parents also, stiltz cleaner, Standard Oil
Mary Paradzina, 40, unknown when arrived, alien, born in Austria (Croatian), parents also
John Mlynarycz, 17, son, single, born in Pennsylvania, shipbuilder, shipyard
Rose Mlynarycz, 12, daughter, born in Pennsylvania
Cecilia Mlynarycz, 6, born in Indiana
Frank Mlynarycz, 4, born in Indiana
https://familysearch.org/ark:/61903/1:1:MFWW-ZXV--------------
So the family was only in the Hermanville, Michigan, area for 4 or 5 years. During that time, presumably, they became close enough to Mary Francis Sloan, born 1912, in Hermanville, to call her a sister and for her to call their children nieces and nephews.
We have found five of the nieces and nephews mentioned in Mary Francis (Sister M Agatha) Sloan's obituary, and they are all grandchildren of John Minarich/Mlinaric + Mary Krazovich/Krznarich. So this is definitely the right place for me to look.
I haven't found Mary Francis or Nick Minarich yet in 1920, it was getting late last night. I'm thinking she and the missing Minarich children are in an orphanage or home for children somewhere. - Also I plan to browse that 1910 Meyer, Michigan, census for Sloans.
Thank you everyone for the help.