On our last trip we did almost exactly what you mentioned, family of 4, two weeks, mid-June with one teenager. We flew into and out of Shannon and stayed on the west-southwest coast.

I would not abandon Michele's idea to rent a house for at least one of the two weeks. You could still do your castle stay, working farm and B&B's. Having a base such as Killarney in the southwest would give you an opportunity to do a few day trip coach tours so you would not be "driving all the time". Having a base you would not be living out of a suitcase all the time.

I mentioned Killarney as a base because you could certainly fill a whole week from there. Also, Killarney would be a good place for golf and horseback riding through Killarney National Park. It has great scenery and history. It is only a two hour drive to Blarney or Cobh if that would interest you. Bus coach tours are available to Dingle and around Shea Head and another tour around the Ring of Kerry. There is a day tour through The Gap of Dunloe by horse and trap with a boat ride on the Lakes of Killarney. Within Killarney National Park is Muckross House and Garden, Muckross Traditional Farms, Torc Waterfall and the restored Ross Castle with a great educational tour.

You could also head up to the Galway/Mayo area and stay a night at Dromland Castle in Co. Clare or Ashford Castle in County Mayo. Be aware you are talking around $700 to $900 per night for your family of 4, unless you get a special deal. On your way up to Galway you could stop at Bunratty Castle and Folk Park near Shannon and the Cliffs of Moher. From Galway you could take a ferry out to Inis Mor to tour the island as a day trip. Also great scenery in and around Connemara.

During the time of mid-June you will have about 17 hours of daylight with sunrise around 5 AM and sunset around 10 PM. To me that is the best time to be in Ireland. Although I would be happy to be in Ireland at any time.

If you would decide to do a house rental there are other tips the forum members can give you, just ask.

One of the best parts of your trip will be the planning and you have lots of time, enjoy.

Coming onto this late on here.. Flying into either Dublin or Shannon you could consider having the first day somewhere close to arrival or get the bus from the Airport to Cork for night one.  Pick up a car at Cork airport the next morning and drive the Wild Atlantic way as far as Sligo before heading back near the departure airport for the last night. http://www.failteireland.ie/News-Features/News-Library/Your-views-sought-to-shape-Wild-Atlantic-Way.aspx  maps in the View the rout section on that page.