Shannon to Aran Islands

Doolin is probably the best place to get a boat tour from. This is about 64km from Shannon.....

First question - how are you planning to get to Doolin? Hiring a car and driving off a Transatlantic flight isn't very sensible. Even if you have slept on the flight you are likely to be jet lagged and tired. Hiring a car and driver for a day is going to be very expensive. (Catching a bus is a non runner as you can't get to Doolin in time for the 11 am boat trip trip).

You would need to arive in Doolin in plenty of time to catch the 11am ferry to either Inis Mor or inis Oir. The last ferry back is 16.15 from Inis Mor or 16.45 from Inis Oirr. You will get back to Doolin around 5pm. It will take about an hour to drive to Ennis.

So theoretically it is possible. Is it worth it? Only you can decide that. Remember it could well be a long and tiring day (you can't guarantee weather either) and are likely to end up tired even before beginning your RS tour...

Another way, and you would need a lot of luck- with a slightly early arrival and fast immigration is-
the 0754 bus from Shannon to Galway, arrive 0945, the 1030 airline connection bus to Connemara airport, then the 1130 flight over, the last flight back, and the hourly bus Back from Galway to Ennis- 75 minute journey.

The problem is that you would need to book the Connemara flight but can't foresee whether you could get there in time.

It is 76 miles from Shannon to Connemara airport so a hired driver should do it in about 1:45 (so leave Shannon around 0830, 0900 at a squeeze) but at a cost. Even then you can't afford for the flight to be significantly delayed.

On a jetlag recovery day, with a tour to join next day this feels like a lot of energy being expended.

That does sound a high stress option isn31c. I don't think I would want to chance that...