Hi,
My great-grandfather was Martin Francis J Byrne (B: 1859), son of William Byrne and Bridget Clark, from County Dublin. I assume my GGF's brother is your great-grandfather Stephen.
If so, Martin Francis J Byrne immigrated to Australia at some point. He was married to Mary McCready (B: 1960 D: 1940) of Fairfield, New South Wales, Australia. He had 11 children.
My grandfather, Martin Luke Byrne (B: 1905 D: 1981) was their youngest, born in Sydney. He had 14 children.
My father, Vince Paul Byrne (B: 1936 D: 2019) was their youngest, also born in Sydney. He had 2 children, and i'm their eldest.
So, we are extremely distantly related if that's all correct.
Hope this helps fill in some blanks!