We have at the moment Patrick (b. 1881, Kilderry, Co. Galway, eldest of 11 children) married Fannie Jackson (b. 1881, England), emigrated 1904, then in the US censuses of 1910, 1920 and 1930. They had sons Martin (1907-1930), Patrick (1908), John (1912), Peter (1914) and Thomas (1917). But we didn't find them in the 1940 census, so we know nothing after 1930. A Fannie Fahy was buried in a Philadelphia cemetery in 1943, but that might not be the right person. Anything you can add to this would be fascinating.
The DOB you gave for Patrick is inaccurate relative to the baptismal register in Peterswell, but this isn't surprising. Several of his relatives were just as unreliable in later records. I suspect they just didn't know, and therefore guessed.
From what you wrote above, Patrick (b. 1908) married a Kathleen and had the four children you mentioned. This is news to me. We traced the descent from the other 10 children of Martin Fahey and Mary Glynn, but drew a blank with Patrick, after 1930. Amazingly, Patrick (b. 1881) is my father-in-law's uncle.
For interest, I attach what may be a picture of Patrick in a hurling team photograph of 1898. I cannot promise at the moment that this is the right person, but there is a fair chance that it is.