As regards the 'cousins' in Dublin I have evidence of a Bond dated 18 April 1673 between a Thomas BROWNE of Drogheda in Ireland and a Jonathan WILSON of Burton, Cheshire.
Bishop WILSON's mother had a brother Thomas BROWNE (b1634 Burton); his father had a brother Jonathan WILSON (b1630 Burton). So the indications are that the Bond was between two of Bishop WILSON's uncles - one paternal & one maternal.
I believe that Drogheda is some 25 miles north of Dublin, and that Burton was a major port for traffic between England & Ireland at that time.
Any children of Thomas BROWNE of Drogheda would have been cousins to Bishop Thomas WILSON.