Have you checked the timetables at www.irishrail.ie? If you took day trips from Dublin to Cork, Killarney, or Limerick, you would spend most of your time on the train and have very little time for sightseeing. And a day trip to the Dingle Peninsula would be impossible. First, you can only get as far as Tralee by train. From there you'd have to take either a bus or rental car to Dingle and you would literally have NO TIME for sightseeing.
After you've seen what you wish in Dublin, I suggest you rent a car and drive to the Southwest. Base yourselves in either Killarney (full of tour buses) or Kenmare (my preference) and take your day trips from either town.
If you can arrange to fly into Dublin and fly out of Shannon, you wouldn't have to backtrack to Dublin.