The father of the Rev. Josse Glover was one Roger Glover, pewterer of London, who died ca. 1634. (Rev. Josse Glover left a number of New England descendants.) See pedigree chart from Wikitree showing all descendants of Roger:
https://www.wikitree.com/wiki/Glover-1946
First, I question the name Joan for his "first" wife. George E. Littlefield _The Early Massachusetts Press, 1638-1711_, p. 19, discussing Josse Glover as the "father of the Massachusetts Press," notes of his parentage that "Roger Glover, Esq., of Beckett or Bewcott, Berkshire County, England, married Susan, daughter of Robert Goodwin, citizen and salter of London." For this, Littlefield cites the 1610 will of Robert Goodwin, which, however, actually only speaks of "daughter Glover" and "son in law Roger Glover."
https://www.google.com/books/edition/The_Early_Massachusetts_Press_1638_1711/PL938id8VgkC?hl=en&gbpv=1&dq=glover+bewcott&pg=PA19&printsec=frontcover
Because Robert Goodwin only mentions two children of his daughter Glover, i.e. Susan and Ellen Glover, I had questioned this marriage as applying to the father of Rev. Josse. However, in a contemporary controversy over Bewcott/ Beckott/ Beckett and Shreenham / Shrivenham, Roger Glover was paired as a defendant with Peter Goodwyn, a known son of Robert the testator of 1610.
https://www.google.com/books/edition/Lists_and_Indexes/GAbgAAAAMAAJ?hl=en&gbpv=1&dq=%22roger+glover%22+goodwyn&pg=PA372&printsec=frontcover
Also, the 1634 Visitation of London shows that Valentine Mortoft married a daughter of "Roger Glover of Beaucott Com. Bucks," specifically Elliner, very probably the same "Ellen Glover" named as a granddaughter of Robert Goodwin.
https://www.google.com/books/edition/The_Publications_of_the_Harleian_Society/hSjvAAAAMAAJ?hl=en&gbpv=1&dq=glover+moretoft&pg=PA113&printsec=frontcover
The 1664 Visitation of London only assigns one wife to Roger Glover, pewterer, who died in 1634: an "Ann dau. of .... Vandeplanck."
I believe this is a first wife of Roger, and explains the origin of the name "Josse" for the Reverend, i.e., an Englished form of the common Dutch male name Jos or Joos. Ann Vandeplanck is indicated in the 1664 Vis. as mother also of Roger's known sons Roger, John, and Ralph.
Roger Glover, citizen and pewterer, also had property at Walthamstow, Essex, in addition to Bewcott/ Beckett in Bucks.
https://www.google.com/books/edition/Official_Publication/eJsJAQAAIAAJ?hl=en&gbpv=1&dq=%22roger+glover%22+pewterer+elizabeth&pg=RA3-PA7&printsec=frontcover
Roger Glover and "Elizabeth his wife" were deforciants of property at Walthamstow, showing (probably) that his Goodwin wife was really called Elizabeth, not Susan or Joan.
https://www.google.com/books/edition/The_East_Anglian_Or_Notes_and_Queries_on/08NAAQAAMAAJ?hl=en&gbpv=1&dq=%22roger+glover%22+%22elizabeth+his+wife%22&pg=PA365&printsec=frontcover
Littlefield was able to identify Roger Glover's last wife and widow, another Ann, as a Rolt, daughter of John and Judith Rolt or Rolte of Milton Ernest, Bedfordshire, by locating the funerary monument of her first husband, Francis Barty, in the church of Milton Ernest (see also her will, which names some of her own relations).
https://www.google.com/books/edition/The_Early_Massachusetts_Press_1638_1711/PL938id8VgkC?hl=en&gbpv=1&dq=anne+rolt+%22roger+glover%22&pg=PA20&printsec=frontcover
The 1664 Visitation mentions only one wife, Elizabeth Harris, for Rev. Josse, but it is known from other sources that he was also married to Thomasine Owfield.
His son John Glover is shown as having married, something that was not known from the New England side of things. This may explain John Glover's cryptic statement about a grandmother recently deceased "in Scotland" -- who could therefore possibly be his WIFE's grandmother.