Red-eye into Dublin and then drive

Respectfully, I don't think this is a good idea. Most folks will be in no shape to pull this off safely.

While I will admit I have driven after a long flight before, I have only done so when I knew that I would arrive pretty well rested (flying in business class with a lay-flat bed so I can get something close to a decent night's sleep), and even then, it was probably not the best decision I've ever made.

Do you sleep well in planes? That would make a significant difference for me. The fatigue and stress leading up to a long trip is cumulative, and if you're arriving after being crammed into an uncomfortable seat and severely sleep-deprived, you would be a danger both to yourself and others, whether you're behind the wheel at home or abroad "on the wrong side" of the road. Yes, the motorways in Ireland are less challenging than the small "lanes" but it's still a big change and the impact of your condition on arrival should not be discounted.

How about taking the bus instead, get a good night's sleep, and pick up your car there in Limerick (or wherever you spend your first night), and begin the driving when you're rested and ready? I think you would enjoy that a lot more.

Why would you even ask or put your family in a perilous situation?

The answer is NO it’s not a good idea!

I agree with David. We did it once, in Italy, and it wasn't smart. I think the side roads would have been better because you would have to be more alert. The autobaun just puts you too sleep. If you are sleepy, and suddenly need to do an emergency procedure you nature response will be for a right hand driving and in a left hand driving country that could be deadly.

Thinking one can do something and actually being able to do it are two different animals. In my thirties, I naively flew from the US to London and immediately picked up a rental car to drive to Bath.
The opposite-side-of-the-road driving was just one adverse condition. The roundabouts, the bizarre setup of the manual transmission in the rental car, the inability to see beyond stone walls enclosing the narrow driving lanes in the countryside—all of it was too much.
Particularly after a transatlantic flight with no sleep.
I was never so relieved than when I returned the rental car to the agency at their Oxford location before it was due back.
There’s are reasons why almost no American bank will provide auto rental insurance coverage through their credit card.
I think I know at least one of them.

Here is a possible alternative.

Take the train from Dublin to Limerick that first day. You can still proceed on your way, but your safety factor will be quite a bit higher. I also think your family would enjoy the extra space and ability to move around a bit on the train.

Get a night’s rest in Limerick and then pick up a rental car there.

An added bonus here is that you are leading by example. You are showing your children that their safety is important and a priority. Not just saying it, but doing it is a lesson they will remember.

We are extremely lucky as my son in law is from Ireland and therefore used to driving on the other side of the road but he would never do this on arrival. As suggested take a bus to Galway or.some.other location and then rent a car the next day. I think I read a study that driving while tired is as bad as driving drunk..

The correct answer here (as is usually the case) is "it depends".
We've rented cars immediately upon arrival in Dublin and taken to the road several times with no drama, but then I'm comfortable driving on the left and am able to get a good night's sleep on the airplane coming over so I'm confident that I'll arrive rested, alert, and fit to be behind the wheel without posing a hazard to navigation for myself and others.
If that describes you then I'd say go for it.
If not then I wholeheartedly agree with the others that waiting a day or two in order to 1. shed your jet lag and 2. have a chance to study the local traffic patterns and rules of the road, is sound advice.
I also agree that the mind numbing experience of driving on one of the Motorways will only add to whatever level of fatigue you're already experiencing and be a recipe for potential problems.
My final bit of free advice, having done this about a dozen times in Ireland, is to make good use of your co-pilot for help navigating, watching for conflicting traffic in unfamiliar locations, and generally reminding you to "stay left" at intersections and roundabouts. As was mentioned, your muscle memory is going to be all wrong so having the assistance of another good pair of eyes will help keep you out of trouble until you get the hang of it.

I am with Robert.

Have I done this exact thing? Yes, without a problem - I had 3 adults to help me with eyes on the road (and they did). Was it fun or recommended? No. Would I do it again? I doubt it. The roads were fine and traffic on a November afternoon was not at all bad, plus I had an automatic and experience driving on the left. But after a flight? Do what you can to avoid this.

pick up our car rental at 7:00am

And what time will your body clock think it is? That should be a good clue as to how "doable" it is

No, it is definitely NOT a good idea...

Why would you even ask or put your family in a perilous situation?

Not to mention all the other people on the road

Driving after an overnight flight while being jet lagged, driving on the other side, and being on new turf could be an accident waiting to happen. Some are not bother by those things while others (self included) shouldn't be allowed near sharp instruments.

And the final score is -------- NO - 9, YES - 0, MAYBE - 2. And the NOs have it by a wide margin. Good luck !!!

If you haven’t driven on the left and if you’re not familiar with the country, then I’m another no. If you’ve driven that route previously and comfortable with driving on the left, then it’s possible, but only you know your limitations.

Thank you SO much for those of you who responded kindly and with such helpful insight. I REALLY appreciate it!! We have decided to take the express bus from DUB to Limerick that morning. Thanks again!

Good choice, shoretools! As you've probably found out, the bus directly from DUB will be much easier and probably also faster. And you can either enjoy the scenery or sleep off your jetlag, or more likely both, on the way. Have a great trip!

I am so relieved you are taking the bus to Limerick! We know a family who rented a car in a country that drives on the left side of the road. The husband crossed the line and hit a family in their mini-van head on. It was absolutely horrific. His wife in the passenger seat died, his daughter in the back seat was okay, but very beat up. A toddler in the mini-van also died. It was an unspeakable tragedy all the way around. We are going to Ireland in April/May. This is the only part of the trip I am truly concerned about. I’m not an anxious person, either, but I saw the aftermath of what can happen. It destroyed him and his family….. Everyone - drive safely!

Glad you've opted for the bus. I'm always an advocate of not driving straight after a long haul flight. I flew London to Phoenix at the end of November, an 11 hour flight which was in business so I managed to sleep however I stayed overnight in phoenix before picking up the rental car the following day for the five hour drive to Vegas. The drive was fine as I find jetlag affects me far more on the return journey which is why, despite being more than comfortable driving from Heathrow to home I elected to travel by taxi despite managing a decent six hour sleep.