West Ireland Trip in June

Your overall pace looks OK.

A few general thoughts regarding logistics: Rather than staying in or near Dingle town and then heading down to the ROK, you might consider finding somewhere centrally located between the two, settling in, and just doing easy day trips from there. The stretch between Castlemain and Glenbeigh would be a good choice in that regard. From there it's less than an hour's drive to Dingle, the northern part of the Ring including the pretty Skelling Ring Road, Portmagee (where the Skellig boats depart from), the Gap of Dunloe and Killarney NP. Might be nice to unpack once and be done with it for several days with a group as large as yours.
Galway isn't our favorite place in Ireland, though Connemara is. Since the ferry over to Inis Oirr departs from Doolin anyway, why not just stay there? Would be more convenient to the ferry landing as well as the Cliffs and the Burren.
Clifden is our choice for exploring Connemara. The Sky Road scenic drive is just west of town, and from the nearby village of Cleggan you could catch the ferry over to one of Ireland's better kept secrets - the island of Inish Bofin. Can google it to see if it might be of interest. We enjoyed our day there very much.
If you'd like to extend your drive around the Connemara Loop you might consider heading up to the Doolough Memorial near the village of Delphi. It's an extremely evocative place once you know what happened there, and would certainly be educational for the kids. Puts the history of the famine years into rather harsh perspective.
Many here rave about the Hawk Walk experience at Ashford Castle in Cong. Might want to check that out too.

Hi! Fellow Ireland fan here! I guess my best suggestion right now would be to firm up your plans and get your accomodation reservations made. Seems very late in that regard, especially as you will need more than one room. June is high season for tourists in Ireland and I think you may not get your first choices at this point.
I second Robert’s endorsement of Inishbofin. A hidden gem!

I agree with Robert...it makes more sense to stay somewhere between the Dingle Peninsula and the Ring of Kerry; no point in moving around if you don't have to.

A great suggestion for a restaurant is Rozzer's in Aghadoe, which is about 10 minutes outside of Killarney. It's located in at Killeen House Hotel (more of a B&B, really), and the owners, Michael and Geraldine, are lovely people who really know how to take care of their customers. It's voted the best restaurant in the area. Check it out on Tripadvisor: https://www.tripadvisor.com/Restaurant_Review-g3513836-d1488044-Reviews-Rozzers_Restaurant-Aghadoe_Killarney_County_Kerry.html

Also, I second Robert's great suggestion of driving though the DooLough Valley and seeing the memorial; in addition to the historic aspect, it's a stunning drive. I would also suggest a stop at Aasleagh Falls, which is located at the end of Killary Fjord. We've been there twice...the last time was in June, and the salmon were trying to leap up the falls in droves. If you walk along the trail on the left side of the falls it will take you back to where you're only a few feet away.

Russ

Why Inis Oirr and not Inis Mor? The latter is the main area for these islanders, a quiet stay because the tourists leave in the late afternoon, and there is a museum of value there in addition to the many ancients sites-- stone circles, a tower, a "swimming pool" out of stone right on the cliffs. I spent a week there and it's hard to imagine only one night frankly. Rather, I would stay 1 night in Galway-- it's so busy. Connemara a big yes, for 3 nights.
I would forego the Ring of Kerry in favor of focusing on the areas above.

On our trip last fall, we stayed several nights in Clifden (Buttermilk Lodge B&B), and Mitchell's restaurant was so good we had dinner there 2 nights.