In the 1911 census Patrick's children are living with their step-mother Bridget - is that Kate's sister from the 1901 census? The later census has Bridget as 'head' but notes she is married, so it is not clear if Patrick is dead at this stage.
There are a couple of Patrick Kellys baptised in Galway in 1860 (at least) but without any further information it would be hard to know how to narrow the search.
It goes without saying that adding your family tree here to see what you do and do not have from those 1901 and 1911 census 'shells' would also be helpful.