Hi,
I have some information on the Binghams which may or may not be new to you. My Great-Great Uncle Anthony Kelly was a servant working at the house of Arthur Shane Bingham in 1901. He is listed on that census alongside a woman named Barbara Dean and a woman named Bridget Sally.
Residents of a house 5 in Doolough (Rathill, Mayo):
Bingham Arthur Shane 71 Male Head of Family Church of Ireland
Bingham Ellen 38 Female Daughter Church of Ireland
Bingham Denis 34 Male Son Church of Ireland
Bingham Annie 25 Female Daughter Church of Ireland
Dean Barbara 88 Female Servant Roman Catholic
Kelly Anthony 18 Male Servant Roman Catholic
Sally Bridget 18 Female Servant Roman Catholic
What I can tell you is that my Great-Great Aunt, Anthony's sister, had a child named Denis Bingham. On his birth record, the name is Denis Kelly since he was illegitimate. He was born 28th July 1904, at Mingmore with his mother listed as Maria (her name is Mary on other records) and his Aunt Margaret Kelly also present. It is on the 1911 census we see his surname as Bingham. He lived with his Grandparents on the Kelly side of the family at that point. Given the connection with Anthony Kelly, I suspect Mary/Maria must have come into contact with the elder Denis Bingham and had a son by him. Or indeed another one of the Binghams? This would have been scandalous at the time no doubt. I have no idea what his later life involved.
I can also say that from what I know Arthur Shane Bingham had a reputation of conflict with the R.C. tenants, having one of them shot in the 1870s-1880s apparently. He himself suffered an assassination attempt in 1881. This makes me question how friendly Anthony Kelly and the family would have been with the Binghams? I know the Kellys were on the side of the IRA later on in the 1910s-1920s. It's all an interesting history. Anyway, I'm interested if you know yourself about this illegitimate child Denis?
Cheers,
Tony