7 Aug 1884 death of Bartholomew Malecki, age 11 months, 23 days in the 5th ward of Bay City, of cholera infantum, born in Michigan, parent are Frank and Mary Ann Malecki residing in Bay City
17 Nov 1889 death of Mary Malicki, age 34 yrs, on consumption, born in Poland, occupation is housewife, parents unknown who reside in Poland.
29 Sept 1890 death of Joseph Malecki age 1 day, born in Michigan, parents are Frank and Petronella Malecki of Bay City
I also found a marriage record:
1 Feb 1904 Michael Malecki age 26 born in Poland, son of Frank Malecki and Maryann Jankowski, to Genivia Horzewski or Borzewski age 19, born in Bay City, daughter of Anthony and Veronica Kloss, marriage performed by J Kaminski, Cath priest, witnessed by Andrew Krolinski and Febronia Kormieski of Bay City
So it does seem that Frank was married before and that he married Petronellain late 1889 or early 1890.
I will keep you posted if I find anything else. Please feel free to email me directly