You may want to note that in Ireland, the O that they used in front of their names means grandson of or descendant of - either one, but does not ever mean "son of ". The original name of Broderick or before it was anglicized was O'Bruadair.
An interesting find was an O'Bruadair, born in Cork, who after his death became famous for his poetry on Wikipedia Dáibhí Ó Bruadair ~Beth

The parish priest of this church might know if the poet had any offspring. Scroll down this page ~Anne