I have just returned from a trip to Northern Ireland where I have been tracing the exact same family as you. You are my father's 3rd cousin (or my 3rd cousin once removed, if you like!).
My Great-Great-Grandmother was Mary Caughey (1846-1934.I have so far found the following brothers and sisters of Mary, who were all christened at Dundonald Presbyterian Church:- - Samuel Caughey (born 1849, married Agnes Smylie in 1872 at Great Victoria Street Presbyterian Church, Belfast) - Hamilton Caughey (b 1851, m Letitia Jane Smylie in 1876) - James Caughey (b 1853, m Anne Vance 1881) - Agnes Caughey (b 1855, m Henry Jones 1885) - John Caughey (b 1860, m Agnes Murphy 1891)
The parents of all the above were Hamilton Caughey and Jane Brown.
I found out tht Hamilton Caughey (your Great-Great-Grandfather, my 3xGreat-Gf)was buried at Priory Graveyard, Holywood, the next parish up from Dundonald. Hamilton died 23rd July 1887 at the age of 83. Also in the same grave are his wife Jane (died age 74 in 1892) and his son James (died 1921 age 62) with his wife Annie (nee Vance, died 1936 age 82).
I am sure there is much more to find but I ran out of time on my visit! Although I am in England now, I was born in Dundonald myself (left as a baby).
I also found details of another Hamilton Caughey down at Ballygowan at the same time so this might be a cousin of our Hamilton Caughey. Ballygowan's not far and Hamilton is an unusual first name although there are a large number of Hamiltons in County Down (descendents of James Hamilton who was one of the 2 major plantation settlers in Down in the early part of the 17th century).
It's always good to find new relatives so I hope we can exchange information on our respective families as I have a large amount of information on Mary Caughey's descendents (Glenns and Lynchs) who are all related to you.
In any case, I hope this has been of some help and I look forward to hearing from you in due course.