I think I may have found a few records which put the pieces all together.
I found Alvina Klukus in the 1930 census in Jerauld Co SD with her brother in law and sister Otto and Marie Krueger AND Alvina's 1 yr old daughter Shirley.
I found George in Sand Creek Beadle Co in the 1940 census with his wife Mary and son Francis 2 yrs old. He is indexed as "Florge Fireze". Next door to them is the John and Isadore Sexton family.
To me it looked like the marriage to Alvina didn't work out and he married again to Mary Sexton and had at least one son.
Both George and Mary had their SS numbers issued in Oregon which means they might have been on the west coast for awhile.
I found an "Elvise Freese" born in Russia 1906 in Mendocino Ukiah Co California as a housekeeper. She is divorced and has an 11 yr old daughter Shirley! She did not have any other children.
I think tracking down an obit for George is going to be your best bet to find out if he had more children. I haven't gone looking for Francis yet.
The Alvia Freese who died in Colorado appears not to be the correct one. She was with her husband Herman in earlier censuses.
Shirley Y Freese married several times in CA and appears to still be alive.