At the FamilySearch website you can actually find two marriages licences for Dominck Engelmann.
The first one dated May 19th, 1881, lists the marriage of Dominick Englemann (age 22) and Therese Behrs (age 18), and occurred at St. Anne's Church, Town of Lake.
The second one dated September 18, 1888, lists the marriage of Dominick Engelman (age 29) and Lizzie B. Ring (age 21), and occured at St Martin's Church, Englewood.
I have no idea what happened to Therese Behrs, but I assume she either died, or they got an anulment (highly unlikely in that time period, especially among Catholics). Either way Dominick shows up with Elizabeth in census records from 1900 on (the 1890 census was lost in a fire).
I am still looking for records that tell us who Therese was ( I assume she was related to the Behr family, that Dominick lived with in the 1880 census), and what became of her.