What an interesting puzzle. There might be some clues from the mother-in-law and stepsons on the 1900 census. Also his FindAGrave says (without source) that he was married first to Frances Zemanek and second to Josephine Kalinec. He does have two marriage records.
I would probably work first on the WikiTree profile, adding sources and narrative, perhaps in the Research Notes section. Then I would start on the children, not adding profiles but instead research notes, looking for sources that identify the parents. That might clarify things some.
Do you have an Ancestry account? There are several trees that show him with two wives. And one has a family history written for a family reunion. That may have the clues to solve this mystery. {{Ancestry Tree|9499326|6256756905}} It says Josephine Kalinec married John Krc and they had 4 children (Victoria, Frank, Maggie, John) before he died in 1887. He married Frances Zemanek about 1879. Frances died 31 Jan 1889. They had daughters Mary, Rosie, Angeline and three who died young. John and Josephine were married 21 Aug 1889. (in a Catholic church, clue). They had six children Joe, Fred, Annie, Louis, Christine, and Betty.
Wow that history is interesting. If you are related to the family you might want to get in touch with the person who posted it.