I can help with your request at the bottom of this page. John Pope (1791-1863), who married Catharine Uglow, was the half brother of my great-great-great-grandfather Joseph Pope (1803-1895).They had 6 children and you are right to say that John and Catherine had four sons.Here is what I know:
(1) Thomas Alder Pope, b.January 8, 1819 (Bedeque, Prince Edward Island, Canada), twice married, twice a widower, had two children, 1 daughter who died in her youth in France, 1 son Archdale Pope d.1866, converted to Catholicism and was ordained a priest October 24, 1869 at the Birmington Oratory, accompanied John Newman to Rome upon his elevation to Cardinal, d.July 1, 1904 buried next to his son in the Orataory Cemetary at Rednal outside Birmingham;
(2) George Uglow Pope, b.April 24, 1820 (Bedeque, PEI), m.1 in 1841 to Mary Carver (daughters), m.2 in 1849 to Henrietta Page von Somersen (12 children), became a missionary and world expert on the Tamil language, d.February 11, 1908 at Oxford;
(3) William Burt Pope, b.February 19, 1822 (Horton, Nova Scotia, Canada), m. in 1845 to Ann Eliza Lethbridge (9 children), became President of the Wesleyan Conference, d.July 5, 1903 in London. See Moss, Richard: WB Pope: Theologian and Saint (London: R. Culley, 1909);
(4) Elizabeth Pope, m. Rev. G.O.Bate (4 children: Richard, Joan, Elizabeth, Stephen);
(5) daughter? (or perhaps son John Pawley?); and
(6) Richard Vercoe Pope, b.May 28, 1829 (Plymouth, England), m.1 Catherine Rickett (5 children: Mary, Mary-Flora, Anna, Rodney and Lancelot), m.2 in 1868 to Elizabeth A. Phillips (3 sons: Henry Vincent [later Fr Hugh Pope, O.P.], Philip and Francis), converted to Catholicism and taught at the Oratory School at Birmingham, d. 1903? on the Isle of Wight?
John and Catharine were devout Methodists (John's grandfather Thomas Pope(1711-1792) was a contemporary and follower of John Wesley) and their children were all devout.Two became Methodist ministers, one married a Methodist minister, and at least two became Catholic, one a priest.
Dates for John's grandson Fr Hugh Pope: b.August 6, 1869 (Kenilworth), ordained a priest September 19, 1896, d. November 23, 1946 (Edinburgh). [I have short bio if you care]
I would be curious where you got the name John Pawley Pope? I do not know him to be one of John's sons.Also, I did not have the precise date of William Burt's marriage so thank you for that.Hope this helps.Your cousin, Michael Pope