Frederick William's wife was Susannah Barton b.1820.
If you find a person you are interested in in the Hoysted family database, you can click on the link marked "Pedigree" to find their ancestors. You can also find descendants in a similar way, so it's a quick way to establish lines of descent. I think the common ancestor you are looking for is John Hoysted (1755-1808). My line is descended from his son John (1787-1848), and your half-brother is descended from William (b.1792), another of his three sons to his first wife, Ann(e) Richardson. All are mentioned in the first chapter of "The Hoysteds in Australia" posted here on GenForum.