In your original post you state: "Their children were Thomas (?-?), Annie (1850 – ?), Martha (1884-1967, married Theodore Aune), Adolph Jr. (1885 – ?), (Marie (1887 – ?), Louise (1896-1917), Louis Lindahl (my grandfather, 1896 – 1980), Ludwig (1896 – ?)."
Louis is Ludwig.
Annie born 1850 cannot be a child of Adolph, senior, and Marie - since Adolph, senior, was born in 1854 and Marie in 1855. They did have a daughter Anne/Annie, as the records show, born about 1883, so maybe that is what you meant.
What about Thomas? He could be a son who died, if your family stories/family notes contain his name. But if that is your source, and the notes are fuzzy - then it could also be that Thomas is a brother to Adolph.
There's a Thomas Olson in Ashland in 1900 who immigrated in 1880, and if he is a brother, he might be the reason Adolph moved to Ashland. His wife is ANNIE (Anna in 1900 census, below).
1900 Ashland Ward 2, Ashland, Wisconsin Thomas Olson 39, born in Norway, immigrated 1880 Anna Olson 38, born in Norway Mary Olson 12, born in Wisconsin Helmer Olson 11 Alex Olson 9 Harry Olson 7 Arthur Olson 5
I do find a Thomas Olsen immigrating in 1880 - in just a quick look. There is no wife with him and no place of origin (other than Norway) is noted.
Name: Thomas Olsen Arrival Date: 5 Apr 1880 Birth Year: abt 1862 Age: 18 Gender: Male Ethnicity/Race/Nationality: Norwegian Place of Origin: Norway Port of Departure: Liverpool, England Destination: United States of America Port of Arrival: New York Port Arrival State: New York Port Arrival Country: United States Ship Name: City of Montreal