Looking at the 1910 US Census I find that Albert has moved his family to Greenbush Twp (township), Mille Lacs County, Minnesota. He is now a farmer. I also notice that there are only 2 children listed, Otto and Erick. It still shows that Lydia has 6 children, 4 living. So where are Fred and Elizabeth? Fred would be about 25 and Elizabeth would be about 23 in 1910, so maybe they are married and living in their own homes.
First I looked for Elizabeth and Fred in the 1910 Census but was unable to find them. So I looked for marriage licenses because if Elizabeth married before 1910, I will need her married name in order to find her.
I found that Fred, Elizabeth, Otto, and Erick were all married after 1910. So where are Fred and Elizabeth for the 1910 Census? There are a lot of possibilities. One possibility is that since many of the census takers had such bad handwriting, it is hard for the transcribers to make out what the name is. So it could be that it is just indexed in such a weird way, that I haven't found them yet. But I will try looking for them again tonight. (I don't give up easily!)
Here is the marriage information:
Frederick W. Elsner married Lorena Winsor on Apr. 30, 1913 in Mille Lacs County, MN
Elizabeth Elsner married William F Kettelhodt on Sep. 22, 1913 in Mille Lacs County, MN
Erick John Elsner married Lulu Martha Robideau Nov. 15, 1917 in Princeton, Mille Lacs, MN
Otto Richard Elsner married Betty Hedin Nov. 25, 1919 in Princeton, Mille Lacs, MN