Looking into it further, it looks like Thomas Jr. died as an infant, so it makes sense that you were unaware of his existence.
His birth:
NIXON, THOMAS GREER
GRO Reference: 1890 D Quarter in SALFORD Volume 08D Page 99
Most likely, his death:
NIXON, THOMAS 0
GRO Reference: 1890 D Quarter in SALFORD Volume 08D Page 93
On reading your reply, I feel that I have come up with a theory:
Mary Greer gives birth to an illegitimate daughter, Mary Ann Greer, sometime around 1864. She later marries Andrew Hyndman in 1870 and, having not been married previously, she correctly describes herself as
spinster.
When Mary Ann marries, the shame and stigma around illegitimacy (especially in the Catholic community) leads her to making up a father called "
Michael Greer." It is entirely possible that Mary Ann grew up knowing that her biological father's forename was Michael, but she added Greer so it matched up with her surname.
This to me seems a possible explanation of the "spinster" on the marriage certificate and the shared Greer surname. I have to say, people could be wonderfully imaginative when it came to disguising illegitimacy in the 19th century. My great-great-grandfather was registered under the most fanciful reduplicated name (Laurance John Laurance - allegedly after his father), with his father's occupation equally imaginative (teacher of foreign languages). His mother had 2 children out of wedlock, and she registered both with this imaginary father. She left the family soon after the birth of her second child and Laurance was raised by a relative (I discovered his adoptive mother was a relative through DNA). I spent many hours on a wild goose chase after this father, and have come to the conclusion that he was not real.
Whilst there will always be a shred of doubt around whether the father was in fact real, it was through the DNA test that I have 99% confirmed that he wasn't. I tested my mother (Laurance's great-granddaughter) and received not a single Laurance match.
My theory could be completely wrong, so feel free to ignore my rambling response, but if you are truly interested in solving this puzzle, might it be worth testing your DNA? If you have a living parent, who is a generation closer, that would be even better. If you receive a load of Northern Irish matches around the right area that don't seem to fit into any other branch of your tree, it could be through Mary Ann's father.
Queenie
