Ryanair also fly to Trapani (on the Western tip of Sicily) from lots of places including Dublin (no idea of the frequency though) ... might be worth looking at that ... if you are looking at Ryanair connections too don't just look at Stansted .. consider other Ryanair "hubs" served from Dublin for connections.. perhaps Bergamo or Charleroi ... could be cheaper than Stansted.
As stated Siciliy is a pretty big place and Trapani and Palermo are at one end of it .. there's no point in flying there if you're actually heading to the eastern end of the island as it would be a fairly long and expensive ground journy from there to Catania, Taormina etc. (you'd probably need to hire a car as I don't think trains etc. are that much use) ... if you're heading to the Eastern end then Catania is the airport to go to .. as well as the Aer Lingus flights from Dublin you could look at Easyjet and BA from Gatwick to Catania