This doesn't agree with the sequence of events as you have it, but I think you sould take a look at Glen Nelson, born 8 July 1920 to Swan Nelson and Engberg Nelson in Chicago. -- "Illinois, Cook County, Birth Certificates, 1871-1940," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:N77L-RB5 : 18 May 2016), Glen Nelson, 08 Jul 1920; Chicago, Cook, Illinois, United States, reference/certificate 24638, Cook County Clerk, Cook County Courthouse, Chicago; FHL microfilm 1,309,406.
In the US census 1930 Glen's mother is Ingborg G Nelson, and there is a brother Arthur E, born in 1917. -- "United States Census, 1930," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XS5H-JB2 : accessed 25 September 2020), Glen A Nelson in household of Swan Nelson, Chicago (Districts 1501-1750), Cook, Illinois, United States; citing enumeration district (ED) ED 1680, sheet 2B, line 83, family 62, NARA microfilm publication T626 (Washington D.C.: National Archives and Records Administration, 2002), roll 487; FHL microfilm 2,340,222.
Glen Nelson died 29 April 1994, there his mother is recorded with her maiden name, Ingeborg Bergstrom. -- "Illinois, Cook County Deaths, 1878-1994," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:QV92-NYXN : 17 March 2020), Glen A Nelson, 29 Apr 1994; citing Chicago, Cook, Illinois, United States, source reference , record number , Cook County Courthouse, Chicago; FHL microfilm .