Here is part of what I have to establish Honora Wolverston Stapleton as the daughter of Captain William Wolverston.
Honora's aunt was Honora Geoghegan O'Brien Mathew, d. 1735 in Ennis, Clare. Honora Geoghegan was the eldest daughter of Conly Geoghegan of Donore, Westmeath, and his wife Margaret O'Brien. Honora Geoghegan's first husband was Col. John O'Brien, the third son of Murrough O'Brien, first Earl of Inchiquin. John O'Brien died in 1708/9. In 1710 she married as he second husband Thomas Mathew of Annfield, Tipperary, who died before her. Honora Geoghegan's sister Joan Geoghegan married Lt. Col. Terence O'Dempsey, and their daughter Alicia O'Dempsey was the first wife of Thomas Mac Gorman of Inchiquin. Honora Geoghegan's sister Marcella Geoghegan married "Captain William Wolverton of the County of Westmeath," according to the same historical article. These relationships are discussed in "Inchiquin, County Clare" by George U. McNamara which appeared in the Journal of the Royal Society of Irish Antiquaries 31.4 (dec. 1901), pages 357-362.
A claimant to the title of Lord Inchiquin had to prove that Honora Mathew and her first husband, Col. John O'Brien, had no children, and for that reason a certified copy of Honora's will is reproduced word for word in the House of Lords "Case of Lucius, Lord Inchiquin, Claiming the Right to Vote at the Election of Representative Peers for Ireland" (1861), which can be found online in Google Books. In her will, Honora Geoghegan O'Brien Mathew leaves a good deal of money and possessions to her "beloved niece Honora Stapleton, widow of Bryan Stapleton, gent, of Ennis, County Clare," and to Honora Stapleton's four children, whom she identifies by name: William, John, Ellen, Honora.
The smoking gun: Exchequer Court of Equity Case dated 5 Feb 1733, William Bell vs. Honora Stapleton als Wolferston, Christopher O'Brien, Thomas Gorman, William Stapleton, John Stapleton, Ellen Stapleton, Honora Stapleton, and John Hickie and his wife Elizabeth.
So Honora Wolverston Stapleton was Honora Geoghegan O'Brien Mathew's niece because she was the daughter of Honora G O'B M's sister Marcella Geoghegan who married Captain William Wolferston.
I also have reason to believe that the two Captain William Wolverstons in your pedigree are the same, but I will save that for a separate post.