In the early 1860's, William Rummens was widowed with several children. He went to Iowa with the intention of obtaining land, then returned to Wisconsin to get his children and move them to Iowa. In the 1870 census, He is listed in Iowa, with a woman named Jane in the position normally occupied by a spouse, and with several children with a different last name, transcribed as Kurwint, and all were born in Wisconsin. Jane was born in Holland. Is there any way to check marriages in the area around Madison to see if there is a record of William Rummins having married someone named Jane? By 1880, William is listed as divorced, and Jane and the Kurwint(mispelled, I'm fairly certain)children are gone. The family has no record of a second marriage for William. His first wife, Eunice Caroline Hart, was from NY state. They were married in NY and she died in Wisconsin in about 1862.

The Wisconsin pre-1907 vital records index can be found here:
http://www.wisconsinhistory.org/vitalrecords/
If you don't find the marriage there, there is probably no civil record of it, and you'll have to search for a church record.

Thanks for cluing me in to a great site! Unfortunately didn't find what I was looking for.