Aerlingus fly to Catania on Sunday mornings from Dublin. Not sure about Cork or Shannon. I don't think they fly back on Friday's though so you may need a solution via Naples or Rome.
Looking at where you are stying, there does not seem to be much around you. You are away from the most tourist parts of the island by way of Taormina/Giardini Naxos etc. Rural Sicily is just that - small very traditional mediteranean villages. You certainly wont get lively with night clubs etc. Saying that, it is a beautiful island and well worth a visit.