Learning to drive in Ireland

Should we do public transportation to Kinsale and then pick up a one-way car hire from Kinsale to Dingle and then Galway, then public transportation back to Dublin?

Yes. Unless you have some high-priority stop planned between Dublin and Kinsale/Galway and Dublin, you should do exactly that. Both are served well by convenient bus/trains that you would enjoy much more than that long drive.

Some wrong-side driving tips:

Drivers need a Copilot/Helper. This is a critically-important, FULL TIME job. As you can imagine, driving in Ireland, especially in the small places, with small roads (and that's much of the country) can be very demanding at times. It requires concentration, attention and skill – and that's just the physical control of the car (what most of us accomplish every day at home without even being aware of it). Secondary tasks needed for long drives in unknown places, like navigation, fiddling with your phone/GPS app, paper maps, rolling the tunes, and other things, are best handled by the Driver's Helper – their Copilot. Just as much as the driver, your Copilot isn't just a passenger: they need to be an always-engaged, active participant, helping the driver judge left/right distances and help them make adjustments for safety (how close is that stone wall next to the pavement?, how close is oncoming traffic?, etc.). They should also frequently (but politely) offer regular reminders to "drive on the left!", especially after the driver comes to a stop and makes a turn; it's so easy for old habits, muscle memory, and "autopilot syndrome" to steer you onto the wrong side of the road with disastrous consequences.

More Copilot tasks: offering proactive, active navigation instructions and advance warnings of any upcoming turns, merges, roundabouts or hazards they spot up ahead. Also making sure that anyone else in the car is not pestering or distracting the driver; managing snacks or drinks or anything else they can do to let the driver concentrate 100% on just...driving...the...car... and nothing else. The Driver's Helper/Copilot role needs to be taken seriously: as seriously, in fact, as the potential head-on collision at a combined 120 mph that everyone in the car surely all want to avoid.

Be especially careful (a gentle understatement) in the first few minutes, and the first hour, that you get behind the wheel. That's when you have to work hardest to counter the old habits and autopilot, it's by far the most dangerous time to drive. Stay hyper-focused on just...driving...the...car for a good while before the driver/helper mix in ANY other tasks. Do the same thing the next day you get in the car and begin overcoming habits again. And when you get home, back to the familiar land of correct-side driving, be careful then too, the switch back will throw you off a bit initially.

Good luck. Take it slow, be very careful, it'll start getting a bit easier after a while.

You will be surprised once you get behind the wheel how easy it is, but it’s best not to pick up your car right after landing. Wait until the next day when you are rested.

I am unaware of any videos or tutorials for learning how to drive on the left side of the road. But I can give you a couple of ideas for how to get used to it once you are in Ireland. First, don't pick up your car upon arrival at the airport. As you already seem to realize, you won't need it in Dublin and if you found a place to park it in Dublin it would probably be quite expensive. Just walking around Dublin your first couple of days will start to give you an idea of what it might feel like to drive. One thing you could also do is ask to sit in the front seat of a taxi so you get more of an idea of what the road will look like.

A number of the rental car agencies will, for a fee, pilot you out of the rental agency and on to whatever main road you will be initially using. Once you have the car and are on one of the divided highways you won't have any difficulties. If you can, find a parking lot or find a stretch of road that is empty. Move the car around the lane or parking lines so you can get an idea of how wide the car is by either lining up the lane lines with part of the car or feeling the lane bumps on the wheels.

Don't try to navigate and drive. Have a co-pilot be your navigator. The co-pilot is also in charge of reminding you to stay left or, which frequently happens, remind the driver they've moved too far left.

A couple of things to remember when driving, or walking, is to always look right. So when entering an intersection look right, left, right (opposite of the left, right, left you use at home). Cars in the roundabouts have the right of way. Use your turn signals when you will leave a roundabout. And if you miss your exit, don't panic, just go around again. There is no left turn on red (like the right turn on red in the U.S.).

You can preview your driving route on Google Maps using the satellite function.

I don't mean to scare you but be careful driving down to Kinsale. The road down to the waterfront - where most of the restaurants, pubs and B&Bs are, is quite narrow and steep. Parking can also be a challenge if your accommodation doesn't provide it.

Finally, relax. You are not the first person to drive on the left side in Ireland for the first time.

I found this drivers ed Ireland website very useful. You can download the manual which teaches all the rules and road signs and markers.
https://www.rsa.ie/services/learner-drivers/resources/rules-of-the-road
Also, search "Driving in Ireland" in YouTube. There are several "how to" videos, some good, some not so much. There's also a lot of driving tour videos that I used to familiarize myself with how the road looks from the car. Arial drone videos aren't very helpful.
Lastly, driving out of the rental car lot at Dublin Airport is actually pretty easy. You're on a motorway where everyone is going the same direction. I also used Google maps to familiarize myself with the route beforehand from the airport to whatever road or motorway I'll take out of Dublin so I'd know what exits to look for.
As others have said, driving in Ireland takes a little getting used to but being prepared will make it easier. The roads are narrow, which requires your undivided attention, but just be mindful and you should do fine. And get an automatic rental car! 😉
Have a great trip!

My suggestion would be to reverse the proposed order of your trip and start by catching the express bus from Dublin airport to Galway upon arrival - takes about 3 hours and will deliver you into the center of town. There are a number of rental car outlets in Galway so you could start the self-driving portion of your itinerary from there after a good night's rest ... returning it to Dublin airport before finishing up with a few days in the city.
There are no rental car outlets in Kinsale that I'm aware of - you'd have to collect one in Cork if you choose to go that route.
Taking the bus would allow you observe the driver - ie how he handles the roads, roundabouts, turns, etc. along the way and thus supplement what you may have learned from the few YouTube videos that are available. I've found that previewing my daily routes by using the Street View feature on Google maps is quite helpful in familiarizing myself with road conditions in advance.
Driving on the left is really no big deal but there is a learning curve to be negotiated. For me, it helps to spend a couple of minutes just sitting in the driver's seat learning the layout of the various knobs and switches before setting off - helps to minimize the number of times I inadvertently activate the windshield wipers when intending to activate the turn signals for example. I also take a couple of turns around the rental car lot before setting off into traffic - helps me lower my pulse rate a little and further familiarize myself with the car.
Do reserve an automatic. The default rental in Ireland is a manual shifter so be alert when booking to avoid an unpleasant surprise upon arrival.
And do make good use of your left seat passenger in helping with the navigation. All of your muscle memory from years of driving in the US will be wrong, particularly when it comes to looking for signage and surviving the roundabouts.
It may help to know that I've generally found Irish drivers to be some of the most understanding and most patient on the globe ... especially in some of the scenic rural areas where just having a car will be a pure joy.

The one thing I would keep reminding myself is in a panic situation, you tend to revert back to your old, right hand driving skills.