Driving in Ireland or go without a car

We spent two weeks driving around Southern Ireland. The first day was nerve wracking, but we quickly got used to it. Once we got use to the roundabouts, very narrow streets, and driving on the other side, it was not a problem.

Hiring someone to drive you around may be an option, but I don't think it's one that's widely used, so you may find it challenging to arrange (especially if you plan to do it frequently).

Having your own car provides a tremendous degree of freedom that's pretty much impossible to match if you are depending on public transit or some other kind of "ride". If you are only sticking to places well-served by transit, of course getting around isn't a problem. But so much of the best stuff in Ireland is in places with poor or little public transit options (or none at all). There are usually ways to make it work, but it can be extremely time-consuming (it's set up for locals' needs, not for tourists). If you have limited time and you want to make the best use of it, I think having a car of your own (at least for some parts of Ireland) makes a lot of sense.

Any advice on how to quickly aclimate to driving on the other side of the road safely?

While there is a learning curve to be negotiated I think that if you're a competent driver at home you'll be a competent driver in Ireland. If there are two of you it helps immensely to have your co-pilot assist with navigation, look for signage, watch out for traffic in unfamiliar locations, and generally remind you to "keep left" since all of your muscle memory will be wrong.
The idea of driving on the left was a daunting prospect for me too initially (years ago) but after a half hour or so of getting used to the sight picture from the driver's seat I wondered what the big deal was. Now, I usually take a few extra minutes after jumping in the rental car to check out all of the knobs & switches, adjust the mirrors, mentally rehearse what I'm about to do, and generally familiarize myself with the general layout of the vehicle. Tends to minimize the number of times I hit the windshield wipers while intending to activate the turn signals.
It also helps me to take a few laps around the rental car parking lot before setting off onto the open road. That, plus previewing my driving route using the street view feature on Google maps goes a long way towards lowering my heart rate before I set off for a drive.
Starting out in a more rural location would be a good idea I think - you really don't want to start out in city traffic if it can be avoided. While driving on the rural roads is a pleasure, driving in the city can be an ordeal even for experienced drivers. Maybe in your case consider collecting your car in Galway and then doing a one-way trip up thru Connemara & Donegal before returning the car at Dublin airport. One way drop fees aren't too bad in Ireland - especially as compared to the daily charge for the vehicle itself - so that might be your best option.
Pay extra for a car with automatic transmission and take the full insurance cover for the peace of mind.

Robert gives good advice, as usual. I’ll add just a couple of ideas. First, don’t rent a car upon arrival. With jet lag and everything else, you won’t be at the top of your game. Plus, spending a day or two just walking around or riding in a bus/taxi will help you wrap your head around being on the “wrong side”. Remember, look right whether walking across the street or turning in a car or entering a rotary. Cars in the rotary have the right of way. There is no “left” turn on red.

There are also the roundabouts to navigate, which I never mastered but my husband did and he guided me thru them on the days that were my turn to drive. :-o

Hiring a driver might be the best option if you have doubts. We drove ourselves twenty years ago, when we were 20 years younger. Now at our age, if we go back, we likely won't do that because our reflexes are slower.

Lots of people hire local drivers and are very happy.

I will be driving in Ireland for 11 days in a few months and will be driving an automatic. It’s more expensive, but safer. It will be day 3 in Ireland before picking the car up. My first time there I had the car for 4 days, but unwisely I picked it up on arrival and drove 1.5 hours. I swore I would never do that again, especially under driving conditions that are so unfamiliar.

We just used a private driver in May and it was the best decision ever. I did book way back last summer as it was a rebook from a 2020 Covid cancelled trip. It may be a little more difficult to find someone up in Donegal, but I would search in Galway for options. The driver I used did not go past Galway. Due to the high cost of rental cars this year, I think private drivers are more common than you think.

We used public transport only on our trip and had a great time. Ireland is one of the harder places to do this and it did impact out itinerary.

I think that using a combination of public transport and a private driver might be an excellent choice for you. Use public transport when it is reasonable (and there are many places included in this category) and a private driver when it is not.