There is no evidence of the name of Walter's first wife.
Birth 09 Oct 1585 Parham, Somerset, England
Arrival 1621 Massachusetts
Death 10 Nov 1661 Duxbury, Plymouth, Massachusetts
1631 Massachusetts Colony
1634 Middlesex County, Massachusetts
Walter a Separatist Puritan, who in an effort to seek religious freedom left England (sic)--on April 5, 1629,(sic)-- "Walter Palmer sailed on the "Four Sisters of London (sic)" Robert Harman (sic)--as Master from Gravesend, England, arriving in Salem, Massachusetts". 
Walter embarked at Salem Harbor in 1629 where he stayed a short time then removed to Charlestown abt 1631 and is listed as a Founder. He then relocated to Rehoboth in 1642 and is listed as a Founder then on to Stonington in 1652 where he lived out his life. He is listed as a Founder. 
“Now in this year 1629, a great company of people (The Higginson Fleet) of good rank, zeal, means and quality have made a great stock, and with six good ships in the months of April and May, they set sail from Thames for the Bay of the Massachusetts, otherwise called Charles River. The fleet consisted of, the George Bonaventure of twenty pieces of ordnance; the Talbot nineteen; the Lion’s Whelp eight; the Mayflower fourteen; the Four sisters fourteen and the Pilgrim four, with 350 men women and children, also 115 head of cattle, as horses, mares, cows and oxen, 41 goats, some conies (rabbits), with all provision for household and apparel, 6 pieces of great ordnance for a fort, with muskets, pikes, corselets, drums, colors, and with all provisions necessary for a plantation for the good of man.” 
On September 28, 1630 there was recorded a "Jury called to hold an inquest on the body of Austine Bratcher." It found "that the strokes given by Walter Palmer, were occasionally the means of the death of Austin Bratcher, and so to be manslaughter. Mr. Palmer made his psonall appearance this day (October 19, 1630) & stands bound, hee & his sureties, till the nexte court." At a court session of "a court of assistants, holden att Boston, November 9th 1630" numerous matters were taken up and disposed of, including the trial of Walter Palmer and one other item of interest: "it is ordered, that Rich. Diffy, servt. To Sr. Richard Saltonstall, shal be whipped for his misdemeanr toward his maister." "A Jury impannell for the tryall of Walter Palmer, concerning the death of Austin Bratcher: Mr. Edmond Lockwood, Rich: Morris, Willm Rockewell, Willm Balston, Christopher Conant, Willm Cheesebrough, Willm Phelpes, John Page, Willm Gallard, John Balshe, John Hoskins, Laurence Leach, /The jury findes Walter Palmer not quilty of manslaughter, whereof hee stoode indicted, & soe the court acquitts him." The above is the first discovered reference to William Chesebrough, one of Walter's closest friends.
Walter became very prominent in the affairs of Charlestown, holding public office and is listed among the first group of men who took the Oath of Freeman of Massachusetts Bay Colony, Community of Charlestown (sic) on May 18, 1631. The original list included, "Mr. Roger Conant, John Balche, Ralfe Sprage, Simon Hoyte, Rick: Sprage, Walt (Walter) Palmer, Abraham Palmer, Mr Rich: Saltonstall, Rich: Stower, Czekiell Richardson, Wm Cheesebrough.  The trial likely held up Walter's ability to become a free man in 1630 (sic).
Walter was a Farmer and Dairyman.
Walter apparently had a wife or wives before coming to the Americas, her/their names are not yet known. Walter's second wife was as follows: Reverend Eliot's records of the Roxbury First Church state: "Rebeckah Short, a maide srvant, she came in the yeare 1632 and was married to Walter Palmer a Godly man of Charlestown Church." Their marriage date 1 June 1633 is the same date Walter and Rebecca were admitted to the Church of Charlestown. 
Walter died 10 Nov 1661 Stonington, New London, Connecticut, USA and is buried in Wequetequock Burial Ground, Stonington, New London, Connecticut, USA.
Children of Walter Palmer and Rebecca Short
Information developed from Find A Grave Memorial No. 7158495.
S-1734486808: Derbyshire, England, Extracted Parish Records Author: Ancestry.com Publication: Online publication - Provo, UT, USA: Ancestry.com Operations Inc, 2001. Original data - Electronic databases created from various publications of parish and probate records. Repository: #R-1798358171
S-1738587974: Massachusetts Applications of Freemen, 1630-91 Author: Ancestry.com Publication: Online publication - Provo, UT, USA: The Generations Network, Inc., 2000.Original data - Paige, Lucius R.. List of Freemen of Massachusetts. Boston, MA, USA: New England Historical and Genealogical Society, 1849.Original data: Paige, Lucius R. Repository: #R-1798358171
S-1743966135: Massachusetts Census, 1790-1890 Author: Jackson, Ron V., Accelerated Indexing Systems, comp. Publication: Online publication - Provo, UT, USA: Ancestry.com Operations Inc, 1999.Original data - Compiled and digitized by Mr. Jackson and AIS from microfilmed schedules of the U.S. Federal Decennial Census, territorial/state censuses, and/or census substitutes. Repository: #R-1798358171
S-1774348280: Passenger and Immigration Lists Index, 1500s-1900s Author: Gale Research Publication: Online publication - Provo, UT, USA: Ancestry.com Operations, Inc, 2010. Original data - Filby, P. William, ed. Passenger and Immigration Lists Index, 1500s-1900s. Farmington Hills, MI, USA: Gale Research, 2010. Repository: #R-1798358171
S-1782947960: Connecticut, Deaths and Burials Index, 1650-1934 Author: Ancestry.com Publication: Online publication - Provo, UT, USA: Ancestry.com Operations, Inc., 2011.Original data - "Connecticut Deaths and Burials, 1772–1934." Index. FamilySearch, Salt Lake City, Utah, 2009, 2010. Index entries derived from digital copies of original and compiled Repository: #R-1798358171
S-1791585684: U.S. and International Marriage Records, 1560-1900 Author: Yates Publishing Publication: Online publication - Provo, UT, USA: The Generations Network, Inc., 2004.Original data - This unique collection of records was extracted from a variety of sources including family group sheets and electronic databases. Repository: #R-1798358171
S-1791585754: Millennium File Author: Heritage Consulting Publication: Online publication - Provo, UT, USA: The Generations Network, Inc., 2003.Original data - Heritage Consulting. The Millennium File. Salt Lake City, UT, USA: Heritage Consulting.Original data: Heritage Consulting. The Millennium File. Salt Lake City, UT, USA Repository: #R-1798358171
Baldwin, John D. (1880). A Record of the descendants of John Baldwin of Stonington, Conn.: with notice of other Baldwins who settled in America in early colony times. Printed by Tyler and Seagrave, Worcester, Mass. (pg 13)
" (2) By 1633 REBECCA SHORT "a maid servant, she came in the year 1632 & was married to [blank] Palmer a godly man of Charlestowne church" [RChR 77]. (Wyman claims that Walter and Rebecca were married 1 June 1633 [Wyman 507], but there is no record of the marriage and this was the date they were admitted to the Charlestown church.) She died Stonington 15 July 1671 ("Saturday at night Mother Palmer departed this life" [Minor Diary 93])."
Reverend Eliot's records of the Roxbury First Church state: "Rebeckah Short, a maide srvant, she came in the yeare 1632 and was married to Walter Palmer a Godly man of Charlestown Church."----They were m 01 Jun 1633 Charlestown, Suffolk, Massachusetts, USA
I am having issues with the Rebecca Short marriage the more I look at it. I know I confirmed/completed some of the merges & will admit my screw up (if it was one). Does anyone else find it strange that William would have be almost 50 when he married Rebecca and 65 when he had his last kid? Help? Hate to see this go any further down the wrong path if we are making a mistake somewhere.