The lady in the 1901 census, does seem fairly likely to be Francis's widow given that her trade was hosiery same as the Francis. I also note she was born in Nottinghamshire (as he was).
Francis Spencer is not a very common name in Ireland. I notice that there was a Francis Spencer marriage registered in Balrothery in 1865. It was to Ellen Matilda Appleyard. Not Mary Hardy/Harding. Just odd that there should be a marriage at the time and location you would expect. You might want to look at the certificate to see if he was in the hosiery trade.
Can’t see Mary in the 1911 Irish census. Where were Wrighthall and Robert living at that time? Could Mary have gone to live with either of them and have died there?