There's a great site for Manitowoc genealogy, http://www.2manitowoc.com/
That said, a quick peek there netted me nothing. However, they give various resources for more info.
Ancestry.com has an Anderson Family Tree stating that Jane died in 1856 and William W. in 1858. (It shows two children, Julia N. in 1855 and William Albert in 1856.)
It says that her parents are William Goodwin (about 1800 in NY - 1860) and Amanda M. F. Stout (Sept 18, 1809 - after 1880)
Amanda's parents are listed as John Nesbitt Stout (1771 - 1812) and Anne Holmes (1786 - 1824.) John had been married first to Hannah Price (1772 - 1805) and they had 5 children.
John's parents are listed as Nathan Stout (Jan 1748 - March 10, 1826) in Amwell, Hunterdon, NJ and Esther Ketcham (March 16, 1748 in Monmouth, NJ - June 28, 1804 in Amwell.)
I have no idea about this particular tree, it is unsourced, but I'd advise viewing info on any trees as good clues, but verify the info.
(There's another tree very well sourced that says Jane died in 1856 in Manitowoc and is residing in Michigan in 1860.)
Hope this helps lead you to your answers!!