Your query has been up for years, but I just saw it now. If your John Peter Monschau married Anna Maria Falkenstein, then the marriage record states 11 sept 1832 at Adendorf, Rheinland, Preussen. I have two children for this couple: Heinrich 4 jul 1885 and Maria Josepha 22 dec 1838.
I don't know where life took them, but I think they might have resurfaced in their last days, in WI. Here are some details:
1870 U.S. Federal Census. Wisconsin, Jefferson Co., Watertown. 16Aug1870.
Munschau, John. 70 years old, male. Farmer. Value of realty: $400. Value of personal estate: $200. Born in Prussia. Parents of foreign birth. Ann, 75 years old, female. Keeping house. Born in Prussia, parents of foreign birth. Does this family seem to be a match? If so, then the church in Adendorf would be a good starting point to find the relatives that you are looking for. Good luck!