Dear Jean, I too am a Broderick from Tynagh, Peterswell, Co. Galway.
I believe you are spelling the town's name wrong. It is Athenry, Co. Galway. My grandfather, Michael Broderick, had a brother Martin and a sister Jane. I believe they were all from Tynagh. They were born around the 1830's. Maybe your Bridget is related in someway. The towns around Athenry, Co. Galway were small at the time.
Good luck. J. Murphy