Veronica, the good news is your Thornton and Hamilton surnames are uncommon in Galway, so not too hard to pin down the likely areas they came from. In the Griffith's index, Hamilton occurs in only 5 civil parishes--Ross, Rahoon, St. Nicholas, Moyrus, and Cong, and of those 5, Thornton occurs in only Ross, Cong, and Rahoon (Rahoon and Salthill RC parishes). The bad news is that filmed RC records for Ross begin in 1853 and for Cong in 1870, and Salthill hasn't been filmed at all. However, Rahoon records have been filmed back to 1819 on LDS 0926069. You could give that a try, looking for baptisms of John and Ann's children. Diane