Parish births and marriages for Galway and most of Ireland are on line. www.rootsireland.ie
The counties in red are not on line yet.
with a YEAR +/- 5 yrs. you should be able to find a marriage in Ireland to Vincent Minahan or for herself, the brothers names, and Mary are very common Ann,and Nora not so much
A birth record will give you mother and father's name with
mother's maiden name. Place/Parish
A marriage record will give both of the couples, father's only.
If after 1864+ and civil registration you should be able to find on www.familysearch.org