There’s no Robert Park(e)s in the 1901 census, so presumably he died before that. You say he was alive in 1865. Ballymore is in Sligo civil registration district. There’s 3 deaths registered there between 1856 and 1901 which could be him. One b 1808 & died Jul – Sept 1879; one 1822 – 1867 and the 3rd b 1808 & died Jan – Mar 1884. You might consider ordering all 3 to see if one is the correct one. Location and occupation should help you decide.
You don’t say what denomination the Park family were? Have you searched the relevant parish records for Catherine’s baptism? The civil parish appears to be Emlaghfad. RC baptisms don’t start till 1856. You would need to check with the RCB library in Dublin if the family were Church of Ireland.