Unless you have reason to go to Galway first, why not reverse the order and go from Dublin to Kenmare, Kenmare to Dingle, and then Dingle to Galway?  You would be much closer to the Shannon Airport for your flight.  I have driven from Kenmare to Shannon for a flight, but it was a long haul and was glad that nothing slowed us down.  I decided after that scenario that I would try to stay closer to the airport the final evening of a trip.

Monty

September 15th, the day you fly out, is a weekday. Even with an afternoon flight, I am not sure that I would want to try driving from Galway to Shannon, approximately 45mins to an hour.

By the time you travel from Dingle to Galway, you won't have much time to see any of Galway, really. It will be late afternoon before you would arrive. Perhaps you should explain the draw you have to all three towns on your list. With the present itinerary, you will not have any time to experience the areas hardly at all, with the exception of Dingle.

If I only had four nights and a West coast departure, I would probably do something along these lines:

Sept 9-10 - Dublin

Sept 11-12 - Dingle via Kilkenny, Rock of Cashel, Cahir Castle

Sept 13-14 - Ennis (two nights here will give you time to make a day trip to Galway with a drive up the coast)

This would give you a better "taste" of Ireland than the green blur which you are creating, in my opinion.

You could also substitute 2 Nights in Killarney for Dingle and do a day trip of the Dingle Peninsula

Ennis puts you in a better position for making your flight without any stress

Everyone will have their favorite towns. Dingle is one of mine but not a favorite of Tony's, for example.

Ennis is a mid-size market town. It is a great mid point for a day trip North along the coast, stopping at Cliffs of Moher, a drive through the Burren and in to Galway, if Galway is a must see. I am not sure that you have enough time to do Galway and its environs justice with your narrow window of time.

Michele and I both like Kenmare over Killarney because of its smaller size. However, basing in Killarney for two days has its advantages in that you can still do your daytrip to Dingle and explore the town and its pubs in the evening hours.

It takes close to 5 hours to drive from where you are staying in Dublin to Dingle town. That doesn't include stops along the way for lunch and sight seeing, In comparison, it takes 4 hours to reach Killarney, again without adding in stops for lunch and sight seeing. Galway to the Shannon Airport takes approximately an hour and a half barring traffic issues. By comparison, Ennis is a half hour out on a good day.

The long and short of it is that you have scant few days and a lot of ground you are wanting to cover. You can slow down, shorten your list, relax and soak up the local vibe in a few towns without really feeling the pangs of "missing out" because there is beauty around every curve in every Irish road.