9-Day Itinerary Dublin Galway Doolin Dingle

It’s quite fast— but Doolin-able.
I stayed at Buswell’s which was directly across the street from the National Archaeological Museum and Leinster House. Just walked across the street after breakfast to visit the museum. Kilmainham Gaol is about 1.5 miles west of the O’Connell Bridge and trams and buses near the Liffey River can get your group there. I would stay somewhere in this Dublin 2 area as it will give you quick access to bus/tram transit and the train stations.
You carved out an entire day for Newgrange and that’s wise. Either going by tour or independently by train to Drogheda and then the final 5 miles to Newgrange by local bus or taxi— the outing takes all day. The local bus #163 running from Drogheda train station a few times daily will also drive right by the Boyne Battlefield. If you take the 9am or 9:30 am Express train from O’Connell station to Drogheda, bus #163 will be waiting at the train station when you arrive. Newgrange is a rewarding day trip. Be sure to take time beforehand to see the incredible new museum at the Newgrange Vistor Center.
You can visit the Arran Islands from Galway as well.
People love Galway for an overnight, but I understand you may need to keep moving with this itinerary.
The rest of your trip looks fast but fine.
I would plan to be in Dublin the night before your return flight home. I was just there last week and a severe storm had the entire city shut down with all transit and the airport closed for most of the day. Not likely to happen in the summer, but one never knows these days.
Slainte!

Another option is to move Dublin to the end of your trip. Take the train (or bus directly from the airport) to Galway, spend the night there and then pick up the car(s)/van for your Dingle loop, returning the car(s) to the same place and taking the train to Dublin for the remainder of the trip.

Excellent idea! Rent the car in Galway and return it either to TRALEE ( near Dingle) or LIMERICK or back in Galway and then train back to Dublin. That gets you off the hook of the airport slog from Kerry to Dublin and you’ll pick up a day or two for your journey.
Slainte!