More questions for you:
1) When you “did” Italy, where did you go, how much time did you spend there, and did you see and experience enough that you were satisfied with the results?
2) From where are you leaving for Edinburgh? Are you perhaps flying from Dublin, so do you need to be back at the Dublin airport on March 21, and at what time, to get through Security, and make your flight?
3) How are you thinking about getting from one place in Ireland to another? Rental car? Bus Eriann bus (Irish counterpart to Greyhound, except there’s an Irish Setter on the side of the bus)?
4) Any particular things you want to see/do in the places you’re considering? There may be similar sights and experiences in other places, which might be easier to reach in the 4 days you have available.
Some thoughts - On St. Patrick’s Day, avoid the raucous Temple Bar area in Dublin that night. In September (not St. Paddy’s), there were lots of drunks, and lots of them peeing on the sidewalks. I’d imagine it would be worse on March 17 - not a great start to your visit.
Also, Galway’s my favorite place in Ireland, and I recommend at least 2 nights there. I’d go there from Dublin by bus, but again, do you need to get back to Dublin for your departure to Edinburgh?
Another charming town, very close to the Cliffs of Moher, is Lisdoonvarna. Dingle is wonderful, but with your schedule, I’m not sure I’d even try to see it on this trip. Save it for your next time in Ireland. A fabulous town closer to Dublin is Trim. It has a big castle, a great Indian restaurant, and is convenient for seeing some major Neolithic sights.