Did lots of searching for Edward's brother William Thomas (and his son) without any luck. Several promising leads later turned out to be wrong but will keep looking.
Starting with the family-
Edward “Ned” Hay (c1808-1890) m.(1831) Margaret Ann Taylor. At least 9 children:
1. Edward Hay (c1833-1886).
2. James Hay (c1839-1915) m.(1886) Adelaide Finlay Elder (c1850-1918). Four children: Mary Adelaide (1888-1893), Edward James (1888 Coleraine-1933), Hugh Bellas (1889-1895), Margaret Adelaide (1894).
3. Grace Taylor Hay (c1840-1921).
4. Jane Hay (c1844-1926).
5. Joseph Hay (c1847-1918) m.(1884) Janet Robb (1864-1891). Two sons: Francis Edward Cecil (d.1885), Edward Norman (1889-1943).
6. Margaret Ann Hay (c1851) m.(1881) Joseph Wray.
7. Francis Hay.
8. Robert Alexander Hay (c1858-1886).
9. William Thomas Hay (c1845-1931) m.(c1874) Clara Emily Chandler (c1858). Nine children: Edward William C. (c1876), Francis Robert (1877), John Bertram (1879), Margaret (c1881-aft.1958), Eveleen Clara (1885-1956), Adelaide Louise (1888), Eustace O’Neill (1892), and 2 children (died before 1911).
The above family tree is only a brief outline but let me know if you want full dates, sources, etc.