Better late than never. I don't think that Palace and Pallas are the same Palace East and West are local to New Ross and I remember Pallas as being near Gorey.
As to Mary Kate's parents, I think Thomas and Walsh are too late.
Working from Robert who said his wife was in the infirmary in the 1900 story, I found Mary Kent, New Ross, death registered 1st quarter 1901. This would tie in with no record on 1901 census.
The age at death of Mary, puts her birth at 1857.
I am searching without success so far for record of her birth for 1857.