My records indicate that Cornelia Dutcher married Nathan Alling. My records for Sarah Manchester indicate she was born 10 Nov 1777 and that Gideon died 18th of January 1815 in Chatham, NY where he is also buried. The note on His family record says the following:
Gideon Dutcher was a farmer and his sons assisted him in the summer and went to district school in the winter. About 1815 the family moved to Chatham Co., N. Y., where he died, leaving a widow and 10 children.
I couldn't find any more details on Jane Manchester Dutcher but will continue looking through my records. Your idea that Jane may have been Jannetje makes sense as Gideon's mother was Jannetje Vredenburgh. Good luck on your research.(For some reason I did not receive notice of your post and found it by accident.)