1Horace Wilbur Palmer, Palmer Families in America, Vol. 3.
URL = http://boards.ancestry.com/surnames.palmer/2824.1.1.1/mb.ashx This marriage to Susanna Cooke was refuted by Carlton Palmer Jr.
"3. WILLIAM2 PALMER (William1), born 1638 in Duxbury, Mass., died June 1675 in Dartmouth, Mass.; married Susannah Cooke, born about 1640-44 in Plymouth, Mass., died 1704 in Dartmouth, daughter of John and Sarah (Warren) Cooke of Plymouth and Dartmouth, Mass."2Eugene Aubrey Stratton, Plymouth Colony, its history & people, 1620-1691, p. 335, Ancestry.com, 1 March, 1997.
http://books.google.com/books?id=7TH062rPP2MC&pg=PA335&lpg=PA335&dq=%22William+Palmer%22+%22Susannah+Briggs%22&source=bl&ots=sIf0WyEGGE&sig=my8lgCVt1SfVuSO3D_g7puo-URL = j_I&hl=en&ei=sPWBS7vsJITWsgOr-oCQBA&sa=X&oi=book_result&ct=result&resnum=6&ved=0CBQQ6AEwBQ#v=snippet&q=%22Susannah%20Briggs%22&f=false This shows that William Palmer's wife was Susanna Briggs, not Susanna Hathaway or Susanna Cooke.
"...On 15 August 1633 Robert Barker transferred his apprenticeship status from John Thorpe, deceased, to William Palmer (PCR 1:16). On 2 January 1637/38 Stephen Hopkins was presented by the grand jury for suffering excessive drinking in his house by several men, including "old Palmer," who must have died shortly after the event and before the grand jury's presentment. Widow Palmer and "Widdow Palmers man" were among the testifying witnesses (PCR 1:75).
He dated his will 7 November 1637, proved 13 November 1637 (MD 2:147). His wife Frances had died earlier, and Mrs. Barclay shows hints that he may have had an earlier wife. His last wife was Mary _____, described in his will thusly: "whereas I have married a young woman who is dear unto me." He had left at least two children behind in England, and he had a daughter who had married Henry Rowley, but died before 17 October 1633. His son William Palmer, Jr. married Elizabeth Hodgkins, and by her he had one child, Rebecca Palmer, before he died in 1636, predeceasing his father . By his (third?) wife, William, Sr. had posthumously another William Palmer, born 26 June 1638. Mrs. Barclay gives good reasons for thinking that William Palmer's widow Mary later married Robert Paddock. The son of the young wife Mary, the posthumous William Palmer, married a Susanna, who has been variously confused in published material as Susanna Hathaway or Susanna Cooke. Her correct identity is shown by Carlton A. Palmer, Jr., "Susannah (Briggs) Palmer of Plymouth Colony and Little Compton, Rhode Island," MQ 50:188, as a daughter of John and Sarah (Cornell) Briggs and this Susanna Married (2) John Northway. The family history by Horace Wilbur Palmer, Palmer Families in America, vol. 3 (Somersworth, N.H., 1973), has some significant errors."