Hello Marge, I think I may have a piece of your puzzle.
My great-great-grandfather was Richard McAndrew (b. Ballina about 1850).He married Anne Neary 25 Mar 1871 in the parish of Kilgarvan, possibly at Bonniconlon Church.I have the baptismal letter from Bonniconlon Church for their son, my great-grandfather, Thomas Francis McAndrews (1888-1979).
Their other children are:
Michael James b. 1872 John Joseph1874-1964 Patrick b. 1876 Mary 1880-1929
Mary was baptized on 4 Apr 1880 in the Parish of Kilgarvan, Diocese of Achonry, co. Mayo.Her sponsor was Jas Igoe.
Without any dates on John and Anne McAndrew, I can't guess which generation they belong to.I'd love to know what you are able to figure out.