Robert Barker married Alice Snow, b: 1657 in Plymouth Colony, in December 1681. They lived in Duxbury where they had 8 children. 
Robert Barker was married twice. His 1st wife, Alice Snow, passed away in September 1697. On 7 October 1705, at 54 years old, in Newport, Rhode Island, New England, widower Robert Barker married widow Phebe (Cook) Arnold, 1655–1732. This may have been when he became a Quaker. 
Robert Barker was a member of the Society of Friends (Quakers) at least in the later part of his life. 
"In 1708, the Friends' "Women's Meetings" were held at the houses of John Rogers of Marshfield, Edward Wanton of Scituate, and Robert Barker and Arthur Howland of Duxborough [Duxbury] now Pembroke. ... "
Robert Barker died on 25 July, 1729, in Duxbury, Plymouth County, Massachusetts Bay Province, New England. 
The Great Migration Begins: Immigrants to New England 1620-1633, Robert Charles Anderson, CD Version: Ancestry.com, Tim Farr, P.O. Box 449, Ferron, UT 84523, USA, (435)-384-2514, Page number: Biography of Robert Barker
"Massachusetts Marriages, 1695-1910," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:FH9S-BGQ : 9 February 2018), Robert in entry for Prince Houlan and Deborah Barker, 13 Dec 1706; citing reference p 63; FHL microfilm 423,495.