Hi Brenda  

Oh this is exciting.
So according to your information, Arthur and Emily had more than the five children I have noted in my tree.
I am descended from their son George, who was in the Military Accounts Office in Dublin and died in 1824. George's son, Wm Henry, from his second marriage, emigrated with his wife and chn to Australia.
According to my records and the Dublin Marriage License Index, Arthur 
DUNNE and Jane 
GORDON were married in 1780 and I note that a Hester 
DUNN and William 
HUNTER married in 1785...so this needs further investigation.
Handwritten notes in 1893 by my gggrandfather Wm Henry 
DUNNE, state his father was George who died in 1824 and George's father was Arthur 
DUNNE, a solicitor in Dublin and mother Emily 
GORDON.
I would certainly be interested in your research that Hester was the daughter of Arthur and Emily.  
I will send pm my email address.
Cheers  

Cando