Sorry that you have some bad information -
Capt. Henry Kerley, b. 1632 at Ashmore, Dorset, England, son of William the Immigrant who was born in 1602 in Ashmore, Dorset, England and who was in America by 1637, came to America with his father and mother - Ann White, b. 1602? and who was from South Petherton, Sommerset, England and who married William the Immigrant in 1625 - Henry's sister Mary, b. 1627 at Ashmore, who married at Sudbury Richard Smith, Sr and who died in 1654 at Lancaster, MA - and his (Henry's) younger brother William, Jr. b 1633 also at Ashmore and who married in 1666 at Sudbury, a Jane Unknown with whom he is buried at Lexington - Robbins Cemetery, East Village of Lexington.
Children of Henry and first wife Elizabeth White do NOT include Bartholomew - Henry and this Elizabeth were married in 1654 at Sudbury, MA and their first child b. February 11, 1657 at Lancaster was named according to the Old English naming patterns, for his father, Henry, therefore, Henry, Jr. Their second child named in the same pattern, was named for Henry, Sr's father, William the Immigrant. Bartholomew is cited -
American Genealogical-Biographical Index (AGBI)
about Bartholomew Carley
Name: Bartholomew Carley
Birth Date: 1650
Birthplace: Massachusetts
Volume: 25
Page Number: 70
Reference: Gen. Column of the " Boston Transcript". 1906-1941.( The greatest single source of material for gen. Data for the N.E. area and for the period 1600-1800. Completely indexed in the Index.): 22 Mar 1933, 6185
William the Immigrant, was never an inhabitant of Lancaster. He was one of the first to settle Marlborough while Henry was one of the first to settle Lancaster - where his family met with such disaster in 1676.
Bartholomew is never mentioned as a survivor of the Lancaster massacre 1676, nor is he mentioned as being in Marlborough with his father until 1686 when he married Hannah Unknown and his first son James was born.
The parents you name for Henry are not the William of the Confidence, b. 1621 and Anna King, b. @1625, which would make their having a child in 1632 impossible.
Elizabeth White, daughter of Capt. John and Joanne West White, b. Bef. July 29, 1634 also at South Petherton, Devon, England - we have so far not identified any link to Ann White Kerley, mother of Capt. Henry.
The children of Capt. John and Joanne West White figure greatly in the lives of prominent figures in the early colony through their achievemnts and marriages and are interwoven throughout the Kerley/Carley family histories.
Bartholomew and Hannah become entangled in the family of Henry's second family after his second marriage to Elizabeth Ward, widow of John Howe, Jr in 1677 - and their son William the Mariner, b. @ 1683 who married Mary Bowden, daughter of John and Grace Bully Bowden of Saco, ME. - see marriages performed by Cotton Mather at Boston in 1703 - Bartholomew was an unordained minister and baptised some of the later children of William and Mary, and became wrongly attributed as being the parents of those children.