Martha & Pat,
I believe it might be Doolough that you are looking for and the children's mother's name could be Margaret Bourke. If I am looking in the correct location, John Gaughan and Margaret Bourke married in 1877, may have had a son named Thomas in 1878, again in 1879 and daughter Catherine 1880. There are three good possibilities on the death of Margaret Gaughan, 2 in 1881 & 1 1882. The Mayo County library has a wonderful website with a link to the North Mayo Family History Centre where you can purchase these records; also available on Irish Family History Foundation, both of which you can play around with the church parish records and civil registration records to narrow down the search. There is also a list on line of 1883 Emigration from County Mayo (google it) This lists people from County Mayo and their townland. There are two John Gaughan from Doolough, Kiltane emigrating in 1883; among the others listed from Doolough two other families where on the Australian.
Have either of you looked for naturalization records for John Gaughan or marriage records for Thomas or Catherine to obtain mother's name? Thomas Edward Gaughan married New Bedford, 1906, 562-277.
Cheryl