Swedes love (LOVE!!) to change names, so be aware that this family may have left Sweden with their patronymic (son/dotter) name and only later did they use a surname such as Nystrom. (Nystrøm is the Swedish spelling of Nystrom.)
Mary would have been Maria (or another form of Maria: Maja) in Sweden. Nels would have been Nils. Christine would have been Christina/Kristina/Stina/Cherstin/Kerstin/etc. in Sweden. Peter could have been Petter or Per/Pehr.
I looked at the 1880 Swedish Census CD (an index) and I do NOT find any Maria or Maja born 1870-1872 with a father having a last name of Engholm. I don't see any Maria or Maja Engholm born 1870-1872 with or without a parent named Engholm in the 1890 Swedish Census CD. (an index) I don't see her on the Emibas CD (an index for emigration) or the Emihamn database (another index for emigration), so it is probable that she used Engholm after emigration and not before.
I also don't see any Peter (or Per, etc.) August born 1870-1872 in Värmland or any other place in Sweden with a father named Nils and a mother with a name such as Christina, Stina, Kristina, etc. when I look on the 1880 Swedish Census CD (an index).
At least some of your information seems to be incorrect since these indexes are quite good. I strongly suggest that you try to find more information at the Swenson Center and also the Minnesota state censuses (taken in years not ending with 0), death certificates, marriage applications, and so forth.