An aspect of this doesn't seem "right" to me:The John Hamilton of Ballinamona was a substantial farmer. It doesn't fit this profile for his daughter to be a dressmaker in Liverpool, married at age 16 to a tailor.So, I wonder is this is the correct Elizabeth Hamilton.
The Elizabeth Hamilton who married John Byrne in Ballyoughter on 11-Feb-1846, would seem to me to be a much stronger candidate to be the Elizabeth Hamilton born in Ballinamona in 1821.
I think John Hayes was Church of Ireland and Elizabeth was RC.