At first glance it feels like you will spend several precious days in Ireland seeing it from the window of a plane or car. The itinerary feels very disjointed to me. What are you planning for the 3 days in the Galway area? If one of them includes Connemarra then maybe what you could do is this instead:
Dublin 2 nights
Fly to Belfast - one night
Drive to Portrush,( one night?) or drive on to Derry
Derry -- one or 2 nights
Drive to Galway - 3 nights ( Connemarra on the way there -- this will be a long day! Then maybe one day to the Aran Islands?) Then one full day in Galway is plenty!
Drive to Dingle by way of the Burren and Cliffs of Moher, Take Tarbert/ Kilmer Ferry. Stay 3 nights.
Drive back to Shannon to fly home.
No point of going to Cork if you don't plan to do anything there. You will waste a whole day in this travel. The way you have it planned, you have at least 2 extra partial days spent in airports and renting and returning 2 different cars. I would rather keep one car and spend the time instead seeing the countryside.
3 nights in Dingle will not be too much. It is beautiful -- you will wish for more time there.
Or fly into Shannon, do Dingle and then on to Galway, Derry, Belfast and Dublin to fly home.