I am not researching these families, but have a book with a little information;"Pedigrees of Some of the Emperor Charlemagne's Descendants" by J. Orton Buck & Timothy Field Beard:
"Sarah Dunga, b. ca. 1675-8, at East Greenwich, RI, d. in Bucks Co., PA, 1760; m. (first) in PA, ca. 1697, James Carrell I, b. in Londonderry, Ireland, d. in Bucks Co., PA, 10 Feb 1720."
The only child listed in this book is James II and goes down his line to Alyce Cornell, b. 1910 in Charlotte, NC.
"Sarah Dungan was the daughter of Rev. Thomas Dungan, b. at London, Eng., ca. 1632/4, bur in the churchyard at Cold Springs, Bucks Co., PA, 1687/8, m. in 1663, prob. at Newport, RI, Elizabeth Weaver, b. at Newport, RI, in 1647, d. in Bucks Co., PA, 1697, dau. of Sgt. Clement Weaver, and his wife, Mary Freeborn."
Thomas was the son of "William Dungan, Perfumer, b. ca. 1606, bap. as an adult, 15 June 1628, d. at London, England, Sept 1636; m. at London, 27 June 1629, Frances Latham, bapt. Kempton, Beds., England, 15 Feb 1609, d. at Newport, Rhode ISland, Sept. 1677."
The book takes this line on back to Charlemagne.Please see the entry I just put in the Nottingham Forum.