Cami- hope you and your Mom have a great trip. We’ve one 2 trips to Ireland, one south and one north, but neither have included everything you’ve mentioned. Our first trip (south) was mostly by bicycle, so it took longer than a car, and we went directly from Dublin to Galway (without seeing Dublin), then biked down as far as Skellig Michael, went to Limerick by bus to turn in our rental bikes, then home from Shannon Airport.
Trip 2, last September, we mostly had a car, but went directly again from Dublin Airport to Galway by bus, then clockwise up thru Sligo, Bushmills (seeing the Giant’s Causeway but got cut out of a whiskey distillery tour because they were too full and we’d have to wait for the next tour an hour later, but we had to move onward), a night outside Belfast (staying at the Old Inn in Crawfordsburn), then to Dublin via Trim.
So we moved slower to get all those places, and staying longer at times. Can’t speak about your days 4-6 as haven’t been there, but Skellig Michael itself took us the better part of a day, if you’re going to the Island itself by boat, hiking to the monks’ beehive huts at the top, hiking back down along Puffin burrows, and back to the mainland by boat. You could drive to Dingle faster than the 1 1/2 days it took me, but that still leaves very little Dingle time, and staying at least a couple nights would make it more worth your Dingle Peninsula visit. The next day, Limerick to Sligo, could conceivably be done, but with stops in Doolin AND Galway (including finding a parking place in Galway), seems overly ambitious, unless you’re prepared to pretty much see Ireland through your car windows, and doing virtual drive-bys with really short stops. And maybe you don’t need much sleep and are doing fast meals, but food and sleep will need to be factored in, too. Western and northwestern Ireland, in particular, offer really great restaurants and excellent pub and seafood, worth taking your time to enjoy.
Day 9, just Bushmills to Belfast, is certainly doable, although we went from Bushmills (after the distillery gave us an unworkable offer to wait around until 11:00 AM) to The Gobbins guided hike north of Belfast, than finally getting to the Belfast area very late in the afternoon. Maybe our roadside picnic table lunch also made our pace slower, but we had no time to see Belfast itself that day. The next morning, we drove out of Belfast, in the opposite direction of the rush-hour traffic jams, so really missed the Belfast sights in the city itself. You may have more time on Day 10 to see everything you have planned for Belfast, especially if you don’t need to see anything more in Dublin near the end of that day, having been there at the start of your trip. Newgrange and/or other Neolithic sights are worthwhile, if your itinerary allows.
You could pass through every city on your list by car, but cutting a day or two of traveling, at a minimum, to slow things down just a bit is what I’d need to do to travel at the pace I’ve developed, to have enough time to experience places, rather than do what I’d feel was a limiting drive-by. Maybe skip Northern Ireland this trip, even though the Giant’s Causeway is fantastic? And remember your 2-3 days in Northern Ireland involve having UK pounds for money, and driving in miles per hour, vs. the Euros and kilometers per hour in The Republic of Ireland farther south. . . Not a problem, but remember to allow for those differences. Hope you see what you want to see, with enough time to get there and see it, without too much driving each day.