Keith, The Peter Radermacher that we are connected with came, with his wife Christina and 4 children, in 1863. They settled in Waconia. We found a man in Germany who did a genealogy that took our line all the way back to 1580 when that name first appeared in Bocket church records. I haven't seen Wilhelm or either of the women's surnames in that list.
Cornelius Stacken who came to Carver County in 1863 also, is related to the Rademachers (his wife Anna Rademacher). Perhaps that can be a clue for you. They came with seven (7) children.
From information I have (1991) there are over 1300 Radermachers (with the "r") in Germany (not to mention many spelled without the "r") These are mostly in the Rhineland area in Germany between Holland & Cologne.