Misinformation about this man is spread across the Internet. There are many claims that have no documented source. They include:
That William(1) Palmer Sr of Plymouth and Duxbury was son of John Palmer and Elizabeth Verney born 1585. Closer examination of that record (per research commissioned by Carlton J. Palmer, Jr.) indicates their son William DIED on that date. See also The Colonial Genealogist, XII:3, page 115. Therefore, we are removing William(1) Palmer Sr of Plymouth/Duxbury from said parents and associated siblings.
He was NOT the William Palmer who moved to Newtown, LI in 1656; wife Judith Peake, dau of James Peake of London. This was a different family.
That the first wife of William(1) Palmer Sr was Rebecca (______). There appears no documentation of this name. (It is believed he likely had an earlier wife, but her name has not been documented.)
That by this first wife, he had a daughter Sarah who married Henry Rowley. That he had a daughter who married Henry Rowley and had at least one child, Moses, is strongly suggested by William(1) Palmer's will. But that her name is Sarah, while claimed by a 1988 genealogy, the author of that work provides no documentation of a) such a child so named, or b) of a marriage between a Sarah Palmer and Henry Rowley. Anderson (GMB) names her only "Daughter" and we should go with that. Perhaps research into Henry Rowley might shed greater light. For now, we are changing her name to Unknown with an "aka" of Sarah.
That this daughter, with Henry Rowley, had a daughter Sarah Rowley who married Jonathan Hatch. Henry Rowley did likely have such a daughter, but she was likely from his first marriage. If she'd been granddaughter of William(1) Palmer, Sr., she would have been named in his will, since he mentioned other grandchildren.
That his second wife, and she who followed him to New England, was Frances Bottom, dau of Thomas. Her first name is known, but that she was daughter of Thomas is only conjecture based on similarity of given names in each family, and supposition that she was named after her father's brother Francis. Anderson was not willing to go with the "Bottom" surname and lists her as Frances _____. We should, too, including conjectures in her narrative.
That William(1) Palmer Sr.'s third wife was Mary Trine, a maidservant of his who as a child came over on the same ship as he did. Carlton Palmer admits "Trine" may have been reference to her being his third wife. But again, no documentation exists that his third wife's surname was Trine. That her first name was Mary is concluded from Barclay's excellent article. Therefore, we should call her Mary _____ (as does Anderson), and explain the conjecture and lack of evidence in her narrative.
That he had a son Henry who married in Watertown Nov 1635 Katherine. a) there is no such Watertown marriage; b) William had a son Henry, mentioned in his will, but the language implies this son remained in England.
That he had a daughter Joan Palmer Maunder, bapt 5 Jan 1608 in Okehampton, Devon, England. There apparently is such a baptism for a daughter Johanna to a father William Palmer, but no evidence that it was this William.
Carlton Palmer Jr's work, referenced above, has some good information in it, but much is not cited. Where he cites his work, it appears solid. Otherwise, I don't see how we can go with his claims without additional confirmation. (For example, he suggests strongly-- although admits its not proven-- that the emigrant William Palmer was son of another William Palmer in London, mariner, will dated 13 Apr 1602. (Anderson in GMB does not go with Carlton Palmer.)
In 1956 Florence Barclay produced the definitive article on William Palmer, resolving many of the outstanding problems, outlining the careers of the two sons of the immigrant named William, and pointing out several errors in Savage, particularly the mixing of William (b. 1612) with the man who went to Newtown, Long Island [TAG 32:39-45]... Carlton A. Palmer, Jr., has published several articles attempting to outline the three Williams and their wives and arriving at conclusions contrary to those of Florence Barclay [The Augustan Society Omnibus 9:101-103, 107; MQ 50:188-90]. Unfortunately, his misunderstanding of the meaning of "son-in-law" undermines his own arguments."
This would seem to indicate we should go with Barclay's findings.
I've read Barclay's article; it's solid; Carlton Palmer Jr's work provides SOME additional information, but most is unsourced. I therefore suggest we go with the following for this profile: Jillaine Smith
According to Anderson in The Great Migration Begins ..., William Palmer was born c. 1581, based on the estimated date of his first marriage. His origin is unknown, but may have been England.
William married at least twice (possibly was an earlier marriage). His two marriages, according to Anderson were: 1) Frances Unknown, and 2) Mary Unknown William married Frances in England. She was probably the mother of William, Jr., according to Barclay, and Frances was the mother of William, Jr., according to Anderson. We know by William's will that two, or possibly three, older children remained in England when the family emigrated. Frances may have been the mother of these children, also, according to Barclay, and Frances was the mother, according to Anderson.
He married by about 1606, in England, to Frances Unknown. She died before 1637.
Henry Palmer; remained in England is suggested by William(1)'s will which makes a bequest "if he still be living." He was NOT the Henry Palmer of Wethersfield, CT.
Bridget Palmer; remained in England is suggested by William(1)'s will which makes a bequest "if she still be living." That these two remained in England suggests (but does not prove) they were by a previous wife.
Daughter Palmer (aka Sarah) (without citation), m. Henry Rowley; had at least one child, Moses, mentioned as "Moyses Rowley" in William(1)'s will and is considered a grandson. She died before 17 Oct 1633 when widowed Henry Rowley married Ann Blossom, widow of Thomas.
(possibly) William Palmer Jr. (1) b by 1612 (based on date of freemanship). He might have been by the first wife because he came with his father, and not on the next ship with William(1)'s second wife, Frances. In either case, his parentage is unknown. He m. as "William Palmer Jr" in Plymouth 27 Mar 1634 Elisabeth Hodgkins. William died bef 1638; his widow m bef 2 Feb 1637/9 John Willis, as shown by records in connection with the estate of William Palmer Sr. William Jr and Elizabeth (Hodgkins) Palmer had one child:
Rebecca, b 1635-6, called “my grandchild” in the will; living early in 1651/2 when she must have been about 15—on this date her stepfather complained that she had been molested and hindered in performing faithful service unto her master, Samuel Mayo of Barnstable by the wife of Trustrum Hull of Barnstable; No further record.
William married, by 1637, probably in Plymouth, to "a young woman," Mary Unknown (who was expecting when William wrote his will). Mary married c. 1644-6, second, and as his second, to Robert Paddock; and on 24 March 1650/1, third, Thomas Roberts. Child born posthumously to William Palmer Sr.
William Palmer Jr (2), b 27 Jun 1638 (Barclay claims a transcription error on the part of the Plymouth Colony record transcribers, who said 1634; this error is the source of misconceptions that this William was son of the first William Palmer Jr., but Barclay's article points out that impossibility.) He claimed his inheritance at age 21 on 29 Apr 1659. He was a cooper. He m abt 1662 Susanna ______, parents not found. That they had children, underage at the time of Palmer’s death is reflected in his inventory. He died in Dartmouth, MA 1675; inventory of his estate 30 Jun 1675; no will. No record of his widow, no birth records of their children, but Barclay makes the case for these children:
(eldest:) William Palmer (III), b abt 1663; m abt 1685 Mary Richmond, dau of Edward of Little Compton; 12 children. In a 1683 deed, William sells land that “did formerly belong to William Palmer, of said Darthmouth deceased.” Richmond Genealogy claims this William (married to Mary Richmond) was son of Henry Palmer, but gives no proof.
John Palmer, also of Little Compton who married a sister of Mary Richmond.
William sailed in 1621 aboard the Fortune. He was likely of the London (not Leiden) group of Pilgrims. Palmer suggests he was initially on the Speedwell, and returned to London after that ship faltered, coming the next year on the Fortune with his son, William, age 8. [QUESTION: Is William's age actually listed on the passenger list?] His first wife, Frances, arrived a little later, in 1623, aboard the Anne.
The family settled at Plymouth where William worked as a "nailer." His inventory included a bellows, an anvil, a vice, the tools of nail-making. In 1623, William and Frances received two and one acres, respectively, as their shares of the Plymouth land division. In the 1627 division of cattle, William, Frances, and William, Jr. are 8th, 9th, and 10th on the seventh company list. William was taxed £1 7s in 1633, and 18s in 1634; William and his son, William, are both on the freeman list of 1633.
He received a two-acre grant as a passenger on that ship - one acre for his servant William Carvanyell and one for himself. His son William also accompanied him in the Fortune, but was not yet 10 at the time of the land grants.321 His wife Frances followed on the Anne and received one acre, indicating she was not accompanied by any children over the age of 10. 
Last Will & Testament
Will, dated 7 November 1637 and proved 4 December 1637:
William Palmer of Ducksborrow, nailer, being ill in body" named "my loving friends Mr. William Bradford, Mr. Edward Winslowe and Mr. Thomas Prence my executors"; "whereas I have married a young woman who is dear unto me I desire them to deal well with her but my desire is that my estate consisting of land, household goods, ... may be sold and turned into money all except such moveables as my executors think meet to give her for her personal comfort. Next my estate being wholly sold my desire is that my wife may not have less than one third and if she be with child then another third to be preserved and improved by my executors for that child as mine heir and that if in case she be not with child, then I would have mine executors as in conscience they are persuaded out of the remainder of my estate deal with Rebecca my grandchild and Moyses Rowley whom I love, but not so as to put into their father or mother's hands but preserve it for them till they come to years of discretion"; "somewhat to Stephen Tracy"; "somewhat towards the meeting house at Plymouth"; "young Rowley to be placed with Mr. Partridge that he might be brought up in the fear of God and to that end if his father suffer it I give to Mr. Patridge £5"; "in case my son Henry or daughter Bridgett be living, if they demand it, I give them 40s. apiece if they be living." Further "it was the will of the testator that his wife should be ruled by her ancient Mr. Edward Winslow in her marriage if she look to partake in any part of this estate, otherwise not" [MD 2:147-48, citing PCPR 1:28].
The inventory of "all the moveable goods of Will[ia]m Palm[e]r the elder, taken 13 November 1637, totaled £111 12s. 4d. [MD 2:148-52, citing PCPR 1:28-29].
text describing William Palmer Sr (incorrectly merged in other profile)
William Palmer was a Puritan. He came to Plymouth Colony in 1621 and in 1639 was one of the original settlers of Yarmouth.
↑ 5.05.1"Plymouth Colony Wills and Inventories."The Mayflower Descendant: A Magazine of Pilgrim Genealogy and History. (Vol 2 Pages 147-52) Boston, MA: Massachusetts Society of Mayflower Descendants, 1899- . (Online database accessed January 17, 2015: AmericanAncestors.org, New England Historic Genealogical Society, 2010)
↑ Source: #S15161 Data: Text: Date of Import: 28 Sep 2005
↑ Source: Brøderbund WFT Vol. 3, Ed. 1, Tree #4467, Date of Import: Apr 13, 1997
↑ Source: #S14873 Data: Text: Date of Import: Feb 11, 2001
↑ Source: Brøderbund WFT Vol. 6, Ed. 1, Tree #1134, Date of Import: Apr 6, 1997
↑ Source: #S14873 Data: Text: Date of Import: Feb 11, 2001
Repository: The Great Migration Begins: Immigrants to New England 1620-1633, Volumes I-III. (Online database: AmericanAncestors.org, New England Historic Genealogical Society, 2010), (Originally Published as: New England Historic Genealogical Society. Robert Charles Anderson, The Great Migration Begins: Immigrants to New England 1620-1633, Volumes I-III, 3 vols., 1995).
Walmer, Horace W., Palmer Families in America, vol. III (1973). "This family line is descended from Captain John Palmer of Little Compton, Rhode Island, grandson of William Palmer, Pilgrim of 1621."
For historical context: History of Cape Cod, By Frederick Freeman, pg. 173 - 189
Cleaned up, following guidelines in "Uncertain Origin" (I hope). Question: Is the wife named "Unknown Unknown" staying? The two sources considered reliable, Anderson and Barclay, seem to disagree about her. However, Anderson does not mention her.
Florence Barclay, in “The American Genealogist”, Vol. 32, pp. 39-45, very nicely, using primary source documents, lays out the family relationship between the two William Palmers (father and son) who traveled on “The Fortune” in 1621 and the second son of William “the elder” "the naylor" also named, William, later known as “the cooper” who was born posthumously in 1638 and later died in 1675 in Dartmouth, Massachusetts. Send me a message and I can email anyone the pdf files of her piece.