Somehow I didn't notice in the 1910 census that Klara was living in Minneapolis. Thank you for pointing this out. At least we now know for sure that she came to Minnesota.
I've searched for her return to the US after her father's death, but not knowing her married name, makes it difficult. Finding her marriage in Minnesota I think will be essential.
As a last name, she used Pålmoen (farmname) when she emigtated. The family was previously living on the farm Myhre, and she is listed in the 1891 census as Klara Gunhilda Larsdatter Myhre.
She could also be using her father's family name Nesje, though, I would expect her using Larsen/Larson or Paal(s)moen
(Of cource, we do not know for sure that she ever returned, and I'm searching in Norway as well)