Hi ! I am the son-in-law of the late Bedelia Kelly (daughter of Thomas Kelly) and I can tell you from our own research that the above information which you have found is all correct.
Thomas Kelly was born in Battersea, London in 1879 (we have a copy of his birth certificate here), the only children of his Irish parents to be born here. By 1882 and the birth of Christina, his sister, the family was back in Donabaite, Ireland. He married the widow Alice Dowling (born Alice Ferguson) in December 1911, Alice's own first husband William dying in the early part of that year, followed by the death of Alice and William's son William at the age of just 8 months. When Thomas Kelly married Alice Dowling, she had a daughter Alice (aged 3) and Thomas and Alice went on to have 4 children together - Molly (Margaret M Kelly), Bedelia (my mother in law), Thomas and finally Kathleen. Molly died in about 1972, Bedelia died on 12th January 2006 aged 91 at Nazareth House Nursing Home in Prestwich, Manchester. Kathleen died in the spring of 2004 at the age of 85, her husband Bill Imms having died in July 1982.
Thomas's own death is a mystery. Bedelia always told my wife Shelagh that her father had died during Lent when she was about 18 (which would be 1932 or 1933), but an extensive trawl through the death records in this country has not turned anything up and we are baffled. A Thomas S Kelly aged 54 living in Salford died in March 1933 from drowning in the Manchester Ship Canal (he was born in 1879), and another Thomas Kelly (born in 1879) died in 1932 in Birkenhead, but neither profile seems to fit, although the age is right. It did make Shelagh and I wonder if he could have died in Ireland or perhaps there is some family secret that they did not want revealed !!! It is interesting that others have hit the same brick wall with Thomas's death.
His birth puzzled us for a while until we saw the 1901 Irish census records (we had found the rest of his family by that stage), but it was only on looking more closely that we could see that he was born in London (we had always believed him to have been born in Ireland), and once we found that, obtaining his birth certificate was easy.
We will carry on looking and are always happy to share any information which we have, either here or privately.
Thomas's death is a real puzzle