Does the 1939 register actually list a place of birth?
Wexford and Tipperary are two separate counties.
What's given for Ann's birthplace in the 1911 census? (that's the one most likely to give at least a county of birth or something other than 'Ireland').
Does Ann's marriage not list her father's name and occupation?
It's more common for the eldest son to be called after the paternal grandfather but in any case I don't see how you can assume Ann's father was called John.
You mentioned that Ann had at least two brothers, John and William. What do you know about them. Have you found a more exact place of birth than 'Ireland' for them?