My wife, Christine (nee Alexander) descends from Thomas Alexander, the brother of your Francis, according to oral history passed to her by her great aunt.
Their parents were Thomas Alexander & a widow (Mrs. Plagney, nee Osborne). It was his 2nd marriage. They had 2 sons, Francis & Thomas.
Francis married a Miss Osborne of Esker (beside Dromore) & had the following children - James - m. Miss Sprode of Grrenan. (Could be your Jane Sproule) Archibald - m. Miss Osborne of Esker. George - died unmarried in America. Thomas - died unmarried in America. Mary - m. Issac Gornall of Rosscorr. Anne - John Woods. Rebecca - m. Osborne ? & went to America.
Thomas married Mary Skelton & had at least the following children - Mary - m. John Osborne James Thomas- m1. Mary Jane Osborne m2. Sarah Jane Houston of Ballynahatty (My wife's gg grandmother)
Thomas & Sarah's son, James (b.1857, Dromore, d.1938, Melbourne) migrated to Australia around 1875 & married Priscilla Gliddon.
Is this your understanding?
PS.Also have a biography of your James Alexander (b.1812, d.23/11/1900).