Slow Travel 10-11 day trip to Ireland

Read the RS Guidebook yet?

What are your interests?

Will you be driving?

What do you consider great sights?

Adding to Claudia's inquiry: it would be helpful to know where you're flying in from and when you'd be arriving, ie will it be after a red-eye flight? First trip to Ireland? Do you have any experience driving on the left?
In general my suggestion would be to consider an open jaw (multi-destination) itinerary, flying into Shannon and out of Dublin. Renting a car upon arrival in Shannon would allow you to enjoy some of the attractions of the West of Ireland without running yourselves ragged in the process. With a car you could find accommodations somewhere between Killarney and Dingle, unpack once for 5-7 days and enjoy short day trips from a single home base. There's plenty to see in the area to keep you occupied for a week - especially if slow travel is your preferred pace.
Consider a one-way rental from Shannon to the Kerry airport near Killarney. There are a couple of flights per day from there back to Dublin which would save you a largely wasted day (IMHO) driving back across the island. Dublin is worth a few days, and you wouldn't need a car if you wanted to use it as a base for day tours or short independent trips by train up to Belfast or down to Kilkenny.

We have made 4 trips to Ireland, with a 5th coming up, and always find places for 2-4 nights [we learned on our first overseas trip that unpacking/repacking on a daily basis is a drag, even when traveling light, so we avoid it whenever possible]. You should have no trouble finding 2-4 night stays, especially this far in advance. Lots of ideas I could share but would like to narrow them down after seeing your answers to Claudia's Very Essential Questions first.

Any guidebooks itinerary including the number of nights is just a suggestion. You don't have to follow them. You can do whatever you want.

Plan out what you want to see. Then look for bases to visit from. That's what I do.

We live in California and have booked flights to London.
Arrive London Sep 24 at 10:25 am
Depart London Oct 9 at 4:15 pm
Our plan is to immediately fly from London to Ireland on the 24th. Once we layout an itinerary for Ireland I will book the flight into Ireland. I am expecting that we will be in country (either Dublin or Shannon) by mid-afternoon on the 24th.

We expect to leave Ireland on Oct 5. We will visit Scotland for a few days before coming back home through London.

We will rent a car for the full time in Ireland
I have read sections of RS guide and other advice sites for Ireland. At this point, we are considering flying into Shannon and seeing sights that take us from Galway area to Cork area. We could fly out of Cork or see sites going up to Dublin and then fly out of Ireland from there. It seems there is so much to do in the SW and South of Ireland that we could save Dublin for another trip.
The following areas seem like places we would really like:
• Galway Area - Cliffs of Mohar, Aran Islands, Connemara National Park
• Kallarney Area - Dingle Peninsula. Ring of Kerry, Killarney National Park
• Cork Area - Kinsale, Rock of Cashel, Waterford, Cobn
• Dublin

I hope this provide more information about our trip. Feedback is welcome

I think you just identified your hubs. But you don't have to visit Dublin, you can just drive to DUB airport, drop the car, and fly to Scotland. And I'd caution you about driving on your jetlagged arrival day after an overnight flight, especially on the "wrong" side of the road. I'm sure you could find transportation from Shannon to Galway, and perhaps the next day visit the Aran Islands by ferry so you're not driving till after that.

That said, I wouldn't agree with your son about Dublin. I found it a very interesting place to visit for history, architecture, and culture. You may not have time for it on this trip, but I hope you'll consider it -- and Belfast -- for a future trip.

Agree with Dick's observations on Dublin and jet-lagged driving. With that in mind, you could spend two nights and a day in Dublin. I'd recommend finding a place south of the river, near St Stephen's Green, which makes all the main points of interest [and the best pubs] walkable. Then get your car and hit the road. You could divide the rest of your trip roughly into thirds, SE, SW and W. Have you considered adding some days to Ireland and saving Scotland for another trip? There is so much to see in both ! We've done multiple trips to Ireland and Scotland, about 17 days each. And going back again to each this year. I guess we never tire of them. If you really anticipate additional trips, it's something to think about.

Thank you everyone for the suggestions. I really like the idea now of just staying in Ireland longer leaving Scotland for another trip. Cheers to all

Most here would agree that getting behind the wheel immediately after a long flight from the west coast - sleep deprived and jet lagged - isn't a particularly good idea. In your case it'll be even more problematic given your London layover before tagging on another flight to Ireland. It'll be a long travel day indeed.
My suggestion would be to fly into Dublin and spend a night or two there at the beginning of your trip - both to satisfy your curiosity about the place and to get a good night's sleep (or two) in a real bed before collecting your rental car and hitting the road.
All of the places you've mentioned are great and are worth including in your itinerary. Starting in Dublin and working your way counter clockwise from Galway to Cork would make for a more efficient plan I think ... avoiding having to backtrack if you fly into Shannon, while still permitting a "slow travel" experience.
A one-way rental from Dublin to Cork, and then a flight from there back to London, would simplify your logistics somewhat. Might add that you'll have a better chance of getting a vehicle with automatic transmission in Dublin ... which is what you want unless you're already very experienced driving a stick shifter in left-hand traffic. The default rental in Ireland s still a manual so you'll need to take care when making your booking to ensure that you reserve the type of vehicle that you really want.