Help with Itinerary 9-nights 10-days

Galway is a jumping off point if visiting the Aran Islands or Connemara. Other than that Galway is not an attractive city except for a pedestrian street I passed while on a bus. I say go to Galway as planned and the next day take a direct bus to a spot in Connemara and have lunch before returning to Galway.

An alternative transportation option from Dublin airport to Cork is the bus. There are express busses from the airport to Cork - which would save you the time and effort of getting to Dublin City Center to catch the train. https://www.dublinairport.com/to-from-the-airport/by-bus/all-ireland-bus-routes.

2-night stays are a challenge because they really only give you one full day in your location. Are you planning to get a car in Cork to drive to Dingle? And maybe stop along the way? You don't say what you're interested in. From your itinerary, I would guess you enjoy traveling long distances and briefly visiting mid-sized or large cities. I suggest all six travelers make a list of the sights they wish to see and proceed from there. You have plenty of time to book accommodation.

First, I am making the assumption that you will either have a car at some point - or that you have already checked bus schedules to make sure they work.

I second Trotter about taking the bus from the airport, rather than spending an hour heading into Dublin to catch the train.

I actually might reverse the trip and go Galway (which I thought was a charming town with fun music), Dingle, Cork/Kinsale, Dublin - simply because it will take more public transportation time if you decide to stay in Kinsale and you’ll be coming off your long flight, so better saved till you have rested more. And Galway is a shorter trip for that arrival day. Be aware that Galway-Dingle (or Dingle-Galway) is a long travel day.

I respectfully disagree with Mary Pat's take on Galway. I've been several times, including a few day stay in Galway as well as day visits since then. I really like it.

On the other hand, two nights in each place is a lot of moving around, and really only one full day, plus maybe a part of a day, is the most you will get. But I will not argue with your choices of places to visit. Of course, I could add about 10...or 20...or 30... more, but not in the time frame you have.

I agree with Mike. The other poster about Galway said she only saw Galway from a bus. It would seem pointless to go to Galway and then go out of town just to have lunch. Galway is a fine place to eat or listen to music.
If you are in Galway for only two nights, one day, you will be hard pressed to see anything but Galway and then probably missing some stuff. The museum alone will take several hours. And it is worth it to get some knowledge of Irish culture.
It would be a lot easier if you did not have such a rushed schedule, especially consider it is 6 people. Driving? You would need a car big enough for 6 plus luggage and driving is a concentrated effort in Ireland. At any rate, 6 people mustering for departure is a task in itself.
I would say drop one city and consider hiring transport between those places. Your vacation will go much smoother and happier.

We personally didn't much care for Galway, as it felt to us to be a place that exists only to charm and extract money from tourists. Others clearly disagree. I think "polarizing" might be accurate. We did have very good hamburgers there, which for burger lovers in Ireland is worth noting.