I suspect Jane was a second wife, being so much younger than George.In fact, she might even have been a daughter - the census did not specify.
Google the following:
Full Text of "Goodwin Families in America"
It will bring up an article written in 1899 for the William & Mary Quarterly.See pages 43 and 44 for info on your George.It does not give his father's name, but George's son writes in a letter that George's father was in the Rev. War.