According to my own research Thomas Kelly (1796-1786) owned the Kildare Arms and is buried outside the cathedral. He had at least four sons, Thomas, Edward (your Ned); Waldron and Robert. The latter probably is the Robert Kelly sr. who was stationed in Madras and was killed there in a duel (The duel was hushed up by his relatives and the story spread that he had died heroically in battle in 1790. These Kellys are of great interest to me as Robert was the father-in-law to Gothic novelíst Isabella Kelly (Born Fordyce) who married Robert Hawke Kelly (one of Ned's cousins) in 1789.
Attached the Kelly arms and their Motto turris Fortis mihi deus (God is the tower of my strength)