Rent cottage or stay in hotels?

Your day of arrival doesn't really count as a sightseeing day. Do you have 4 nights after arrival? Or just 3? In either case, I do think your list of destinations is too ambitious for the short time. The other thing is that if you rent a cottage as a home base, you'll be driving long distances each day to "commute" from the cottage to your desired places. And a cottage/house may be available only as a weekly rental, not for just a couple of nights.

RS advises choosing either Ring of Kerry or Dingle Peninsula, not both. People on this site generally say great things about Dingle. I could imagine landing in Shannon and driving to someplace like Tralee as a base for Dingle, then exploring the peninsula the next day so you'll sleep in the same place the second night. Day after that, take the Tarbert ferry to drive to Cliffs of Moher. That night -- is that your Dublin night? Or do you have one more night to go?

Per your other post I'm assuming that your travel dates will be over the Easter break in 2019. If you've not already booked your flight to London I'd suggest just flying there from Shannon to preclude having to waste most of a full day just getting from SW Ireland back to Dublin for your flight. Dublin isn't going anywhere - save it for a future trip. Besides, given the choice between a day in Dublin and an extra day in the West of Ireland I know what most of us would choose.
As was mentioned, you really don't have a lot of time at your disposal so you need to cut back on your expectations regarding just how far you can roam without spending most of your holiday in the car. The obvious outlier is the drive up to the Cliffs of Moher - would suggest deleting that off the top ... you just don't have the time.
If you found a place somewhere in the vicinity of Castlemaine or Glenveigh you could unpack once and settle in for your 3 or 4 days (or nights) and be centrally located enough that your daily drives to explore both the ROK and Dingle wouldn't be particularly long. There's plenty to explore in that area that will more than keep you busy - the Gap of Dunloe, a leisurely drive around the ROK to include the detour out along the Skellig Ring Road ( including the Kerry Cliffs), a day in and around Killarney exploring the NP, Muckross House, etc. , and another day dedicated to Dingle and Slea Head Drive - only 45 minutes by car from Castlemaine, and about an hour from Glenbeigh.
Organizing your trip somewhat along those lines would provide the taste of Ireland that I think you're looking for without running yourselves ragged trying to "see everything".
Staying in a self-catering cottage is our personal preference. We find that we save a lot on meals by being able to eat in and splurging on lunch when we're out and about. We've had good luck using https://www.shamrockcottages.co.uk/ and http://www.kerry-coastal-cottages.com/Properties/Menu.html to find cute little cottages in County Kerry. They even have a few with thatched roofs if you're interested in something like that. Most don't require a minimum stay .

I do think that you itinerary is too ambitious if you have less 3 full days ( assuming you have to make your way to Dublin on day 4) not counting day of arrival from an overnight flight. As previous poster said, based on your short stay and how much you want to move around, I would book hotels/b&bs. What are your absolute must sees?