Thank you. Yes, you have the correct census records.
Carl Johan Persson (Swedish spelling) emigrated together with his first wife Carolina in 1891. According to emigration records in Sweden their destination was Negaunee, Michigan. Carl/Charles' father died in 1925. His "bouppteckning" (probate) states that Carl was living in Negaunee.
Carolina was born January 5th 1861. She married Carl/Charles January 4th 1891 and they both left Sweden in May that same year for Negaunee.
I think this is Carolina's death record from October 12th 1901 (even though parents names does not match...):http://interactive.ancestry.com/60872/44471_355276-02489?pid...
Thea could also perhaps be Althea, Dorothea, Theodora or similar...and Mathilda as you suggest...
There were a couple of newspaper articles in Ironwood Daily Globe of Thea's death since it was so tragic. She was found by Victor Nelson who was a son of the neighbour family. He was living in Marquette at the time but was home visiting his mother. Thea died of smoke inhalation trying to set her house on fire. She was found holding a photo of her late husband.
I was hoping that maybe Charles' obituary could give more clues to who Thea was.