Hi Dan,
When I saw Mary Rose on the English census and realised she was older than John Patrick, who was on the Irish 1901 census, I wondered where she was as she would have been 2 years old.
Found her 1901 North Street (Skibbereen, Cork)
Head David Twohig age 35 born Cork, Ireland Revenue officer.
Wife Hanna Maria age 29 born Cork.
Niece Mary Rose 2 born Cork.
She must have been on a sleep-over at her uncle Dave's, which worked out well for you, as it gives you Michael Dennis Aloysius's brother.

1911 census.
Chapel Road (Middleton Cork)
Head David 45 born Cork, Customs & Excise Officer.
Wife Hanna Maria born Cork.
Daughter Mary Josephine age 5 born Cork.
Daughter Norah Christina age 4 born Cork.
Son John Patrick age 1 born county of Kings (Offaly).

So Sandrapeters863 was on the money.
Both of the sons Michael & David born England & Ireland, fits in with what she told you 7 replies back.
Regards Bernice
He