Help on Itinerary

Hi there

Looks like day 8 you can do either the Ring of Kerry or the Dingle Peninsula both are a full day drive

For a driver look at walkwithme.ie Ray and Mary doing guided walks and driving tours from Killarney
We did some on one of our trips to Ireland and enjoyed it very much
Recommend also their Skellig Ring Tour off the Ring of Kerry

Perhaps you can do parts of the Dingle Peninsula the next day(detour) and via Shannon ferry at Tarbert on your way to Galway but that will make it a another full day driving not only ca .3 hrs

another option
Day 12 -14 Did think about staying in Westport and see Connemara NP and Kylemore Abbey
on your way to there via Clifden from Galway?

and see Achill Island on day trip from Westport one day?

Achill Island is 50km northwest of Westport and worth a daytrip

Perhaps stay the last night in Castlebar if you like and return to Dublin from there

Castlebar is about 20km east of Westport on your way to Dublin

Its a long drive to Dublin from Castlebar perhaps stop for Lunch at the River Shannon half the way to Dublin

Hope some of it fits into your plans

I'm concerned about your first day. It looks like you intend to arrive in the morning and head into the city to see the Book of Kells. This is something you need to book a time for in advance. Which means if your flight is delayed, you will miss your spot. A better idea is to drop your bags at your hotel and go for walk. St. Stephen's Green is a pleasant place for a stroll. Or Grafton Street. Or the campus at Trinity. Even Temple Bar. All are very near each other and free of cars.
Another option would be to go to Belfast immediately since you're not planning to have a car there. I'll defer to Stuart (isn31c), but I think the bus is the way to get there from the airport. I don't think you need to reserve a time at Titanic, so you could definitely do that on arrival. While you can certainly hire a private driver to take you to Giant's Causeway, you can also go with Paddywagon. It's a long day, but they will also take you to Dun Luce Castle. They will also arrange a Black Cab tour for you on return to Belfast (around 4:30/5pm. Other Forum members have mentioned something in between a private driver and the big bus Paddywagon uses, but I don't remember the name.
When the plan includes visiting "heritage" touring, I always encourage folks to find out as much as possible before the trip so they can see as many relevant sights as possible. I would stay as close as possible to where you family lived. Super powerful to walk to same land that they did.
One final thought. You have ALL THE THINGS on your itinerary. Consider slowing your pace.

We're a couple a little older, but love the outdoors and pubs (especially trad sessions).

In five trips covering 14 weeks of Ireland,, all in May, we've never been to Guiness Storehouse, Blarney Castle or Waterford Glass, rejecting them as "too popular". We have gone to equally popular spots (Kilmainham, Newgrange, Kells, Causeway) because they are historic or outdoors. We tried Cliffs of Moher one trip and were so turned off by the tour buses full or tourists, that we did it by boat from Doolin on another trip.

We've been to Temple Bar and surrounds and hated the atmosphere, noise, and drunken crowds. Mostly sing-along drinking songs and decidedly not sessions with few exceptions. You can watch an Earthcam livestream of the music at The Temple Bar to get an idea of the mayhem. The Brazen Head and Cobblestone are far better (still crowded, but polite).

https://www.earthcam.com/world/ireland/dublin/?cam=dublinpub

Our favorite spots of all our trips are mostly outdoors, Neolithic sites or sites with Puffins. That list includes Skellig Michael, Newgrange, Titanic Experience. There are some places like Carrowkeel Tombs and Carey Castle where you are all alone.

Our favorite towns (mainly because the contain our favorite pubs) are Cork, Dingle, Doolin, Galway, Donegal, Belfast. With exhaustive research on thesession.org and Facebook, you can find music in many smaller towns throughout Ireland.

Sorry to post such a scatter-gun of opinions, but I'd have to go back through all my trip reports to be complete. All my reports are visible at http://user.cavenet.com/jgurley/travel/ but be warned it may be overwhelming.