I have a wee bit on this family and I'd like to find out where you fit in.
It is likely that John's father was John Bradley recorded in the Tithe Records for Rathlin for 1823 in Ballynagard townland. And, given the eldest son's name was Neil, that the grandfather was Neil Bradley of Church Quarter, listed in the Agricultural Census of 1803 - I have not been able to find absolute proof of these relationships.
I lost many of my original findings a few years ago but I am fairly certain that John left or deserted the family sometine after the birth of the last daughter, Helen, who was born in 1864.
He moved to Greenock and died next door in Gourock in 1881. The death certificate doesn't name parents but notes that he had had mental health problems for many years.
I have VERY limitted lines from Michael and John, two of the sons, but have at least one line from the eldest son, Neil, right up-to-date.
Hope this was of interest