Re: time of year. We went late August last year, and the weather was about as perfect as one could wish for in Ireland (although anytime is likely to be rainy and chilly).
If your parents don't want to move around, I'd suggest flying into and out of Shannon. Depending on how well your group bounces to life after a long flight, I'd suggest having tea/snacks in Adare Village once you leave the airport, or you might instead enjoy a more formal cup of coffee/tea at Adare Manor Hotel (historic lovely hotel w/ pretty gardens), then head toward the Rock of Cashel (allow a good hour for a tour), then head to Kinsale for the night. Book Old Presbytery Inn (downstairs room for your parents), take a nap, then head to dinner at a close-by restaurant (they make great recommendations......we dined at the White Inn or something that sounds like that.....great seafood meal).
If that is too much hopping around for one day, just check into Dromoland Castle when you arrive (they offer multi-night specials....or ask if you don't find one on their web site). Dromoland is smaller castle, but very nice, then head out the next day to the Rock of Cashel, thru Adare, thru Bunratty (visit the Bunratty Folk Park....good example of what Ireland looked like in the 1800s and there is the Bunratty Castle to also tour), good pubs right outside the folk park, then head back to Dromoland for the overnight. The next day, head down toward Dingle, making that loop and come back thru the Ca-ha (sp?) pass and Connor's Pass.....absolutely lovely scenery, stop in at Kenmare for shopping, bite to eat, then stop by Muckross House to tour, then head back to Dromoland for the night. Third day, head over to the Cliffs of Moher (allow three hours or more to tour, depending on if you take the boat to see from the ocean or if you walk), stop by the pubs in Doolin, then head back to Dromoland for the night. The fourth day, head thru Galway (shop/walk along Key Street (I think I remember the name correctly.....street performers, cute shops, pubs), then head up to the Connemera region for lovely scenery, making the loop.......this will be a really long day. If you can talk your parents into at least one hotel change, stay at Ashford Castle for two nights. That will allow you to visit Kylemore Abbey while you are in the area and arrive at Ashford in time for dinner. The next day book the Hawk Walk for everyone (each person has a hawk and is instructed on launching and landing their hawk). The village of Cong is simple walking distance and has some pubs, some modest shopping. Then head back toward Shannon for positioning for your fly home. We stayed at the Bunratty Castle Hotel (not historic, but reasonable price, clean and easy for easy travel for early morning flights)...or you could return to Dromoland.
If you want to make your life very easy, and if your budget (or your parent's budget allows) contact Tony McGann with Doolin taxi, and have him drive your group. He has a nice van that will seat (I think I recall correctly) 8 people, so it would be roomy for a group of 4. He would collect you on days you need transport and for days that you stay at Castles and want to stay put, you would not need the car. When we traveled with him, he dropped us in Galway for lunch/shopping, then picked us up at a certain time, then took us on up to Connemera....he knew the roads to take, and it was relaxing, as no one had to worry about driving, where to turn, etc. And, Tony is a hoot....everyone knows him, and he LOVES music. His family used to own McGann's pub in Doolin, and he used to run it.
You could also give him some general guidelines of what you want to see, etc. and he will craft an itinerary to meet the needs of your group. He handles all luggage, etc. When he spends the night, he will handle his own overnight, and he handles his own meals.
If one more overnight could be forced on your parents, a B&B in Doolin would make sense.