Hi, welcome to Rootschat!

Just a few random thoughts for now.
You mention MATHERS... when William MULHOLLAND married John's mother in 1879, she was named as Eliza MADDERS.
In the 1891 census, John is aged 17 and his brother James is 11 -
but in 1881 John was 7 and James was 10 - I suspect he was actually 10
months.
Looking for a birth for him, we find James MULLHOLAND (note the spelling!), and the GRO index gives his mother's maiden name as MADDERS.
Looking for other children, there was a William MULHOLLAND born in 1884 (mother nee MCMANUS) who apparently died in 1885. Was this another spelling variation?
Then there's Ellen MULHOLLAND born in 1886 (also mother MCMANUS) - I don't see her at all.

As I said, random thoughts. Perhaps another birth name to search for in Ireland.