Individual Details

Odd to me is that only Prince, son of John & Mary was born 15 Sep 1735, as listed in the Barbour Collection. I suspect Fenner and Prince may indeed be the same son; his name changed. It would be a bit strange to omit the birth of twins. And in fact I did find that he himself possibly changed his name.
http://freepages.genealogy.rootsweb.ancestry.com/~hubbard/PALMER.html

He is said to have married Lydia Buell in Killingworth, but children listed as born in Dover Plains, Dutchess Co NY. Lydia said to be either the daughter of Nathaniel Buell and Deborah Horton, or of Nathaniel's brother Joseph and his wife Anna Colton. No daughter is listed in either of their families in the book History of the Buell Family in England and in America, Albert Welles, 1881. She could fit into either family if the births given for the other children are correct. In examining the records in the Barbour collection, the only Lydia [Lidea Buell] of the right age to marry Fenner Palmer was born 19 Apr 1740, the daughter of Samuel Buell who married "Ledia Willcocks" [Lydia Wilcox, or Wilcoxsin], 1 Jan 1734/5 - but then datases online say that Lydia married a Hoadley.
Lydia, wife of Fenner, was born perhaps 1736-1738, died 18 May 1776, in Hoosick, Rensselaer Co, NY
Sarah, b. 24 Jul 1755
John, b. 29 Nov 1757
Gershom, b. 9 Dec 1759
Anna, b. 8 Mar 1762
Nathaniel, b. 22 Jun 1764
Peter Ward, b. 1766
Fenner, b. 17 Jan 1769
Joseph, b. 21 Nov 1772
Benjamin, b. 21 Nov 1772
Jerusha, b. 7 Mar 1777

Birth

16 Sep 1735

Killingworth, New London County, Connecticut

Father	John Palmer (1705 - 1788)
Mother	Mary Ward (1713 - )
Sibling	Ann Palmer (1730 - )
Sibling	John Palmer (1737 - )
Sibling	Gershom Palmer (1740 - )
Sibling	Ann Palmer (1742 - )
Sibling	Mary Palmer (1745 - )