Dublin to Galway and a whole lot in between

1. Looks like about the same thing. Might depend on rental car company, price, and location of car pick up in both Dublin and Cork. Renting in Cork might be less of a shock to the system than renting in Dublin (but I have only rented in Dublin and driven through Cork - so this is just a guess).
2. The drives won’t be much different than anywhere else in Ireland you might drive. And truth is, you want to see a lot without the extra time to plan for public transportation. So it might be drive or cut your itinerary.
3. I can’t see how without cutting something else.
4. You don’t appear to be going between Dublin and Galway, unless I missed something.
5. Absolutely do not drive at night. Everything is harder in the dark.

This isn’t the sort of trip I would enjoy as much, but the scenery is beautiful between your destinations and if these are the places you want to go and you can handle the one night stays, then don’t feel like you need to travel in someone else’s style. It’s a fast, busy trip, but doable.

Is there a strong reason to be going to Galway from Doolin, only to return to Shannon, apart from that everyone on the forum goes to Galway?
If, on your trip, you want to fit in the Aran Islands then you could stay in Doolin for longer and use the Doolin ferry to any of the Aran Islands- https://doolinferry.com/

It is the shortest of the sea routes.

Galway because husband's actual birthday is during that leg of the trip and he wants to go to some music venue and restaurant there so we figured we'd just end the trip with a couple of nights. However, if anyone has any suggestions for a location around Doolin or the vicinity that has great live music and a noteworthy, indulgent restaurant, I might be able to talk him out of staying in Galway and just doing a day trip there instead.

Driving from Dublin to Cork is a good warm-up for later driving since the roads are easy, well marked, and mostly "freeway". You can return to the airport for the rental or one of the "in town" places, although that option immerses you immediately in more complex driving.

In Dublin, trad sessions are best at The Brazen Head, Cobblestone, the Celt and a few other regulars. Don't bother with Temple Bar as it is crowded and very unlikely you'll find a session (rather than two guys on a stage). Here's some suggested places. Use Facebook to pin down the days.

Cork City Council supports http://www.theleesessions.com/index.php which usually meets at Sin e at 6:30pm. Great trad session.

Clonakilty has a couple of popular pubs including De Barre. The day of the week you're there matters a lot.

Dingle will always have great music. St. James Church has a nice 7:15pm concert that is very session-like and you won't have to compete with loud drunks if you buy tickets in advance. There will be multiple choices for later in the evening.

Doolin is a tiny town with at least four bars that compete for the huge tourist crowds. We happen to like McDermott's best, specially on a Wed night. Your lodging will be able to steer you to the correct bar for the particular night.

Our favorite in Galway is The Crane (upstairs). There are a couple of others on both sides of the river.

All the venues will be crowded, and you have to arrive early to if you don't want to stand all night. My wife is really good at watching people, and sliding into seats when people leave. There are sessions all over Ireland, many in places where there are no crowds, but it takes a lot of research. Facebook and thesession.org are your friends.

We travel with just a carry-ons, so moving between places every day (or two, and rarely three) is easy. Being able to walk to the pub so one can enjoy a beer or whiskey is part of the experience. There are B&Bs on the outskirts of all your selections if you don't mind a long walk, taxe, or designated driver.

In Galway http://www.thecranebar.com/ is one of the best places for traditional music.

"I'm not sure how to get around having to spend the night in those towns/cities (specifically Doolin & Clonakilty) ."
These are two of three destinations your husband has specifically asked to visit. For lots of folks on the Forum, Doolin is a destination.
For folks with Irish ancestry, visiting the home place can be a very powerful experience.
I suggest that you survey your group, and unless one of you is enthusiastic about driving, drop Dingle and use public transportation. Even if you are driving, I'd still drop Dingle. That gives you 2 nights in Dublin, 2 in Clonakilty, 2 in Doolin (with a day trip to Aran), and the last one in Galway. This is still a LOT of ground to cover on such a short trip.
As far as where to rent the car, I'd usually say the Dublin Airport so you avoid the drop-off fee, but you're flying out of Shannon. I'm not sure why, but that's your business. For your itinerary, I'd say picking up at Cork does make sense.
I read this post over several times to see if I could discern when his birthday is, but no luck. Dublin sits at 53 degrees north latitude, which means summer days are long and winter days are short. Very short. As short as 7 hours from sunrise to sunset. You absolutely don't want to drive in the dark, nor after consuming any amount of alcohol.

Sorry, I realize I did leave the timing of the trip out! It's April 17-25 (arriving 17th am). We're flying out of Shannon because it seemed to make more sense than heading back to Dublin but perhaps that is not the case. Doesn't matter though because that's the flight we've booked so we have to work within those parameters.

I would also suggest spending another night in Doolin to visit Aran Islands during the day and more music venues in the evening. I liked McDermott's and McGann's for music and pub food in Doolin; O'Connor's is also very popular. With a car, there are additional dinner and music pubs in nearby towns including th Poet's Corner in the Old Ground Hotel in Ennis.

It is pretty easy to get from Doolin to Galway to Shannon by bus but I don't know where you could drop the car coming from Dingle without going out of your way and losing time.

I thought it was actually a great thought to depart from Shannon with your limited time. Many people forget to consider multi-city itineraries.

After speaking with our friends, we have massaged the itinerary a bit. We're now doing:
Dublin 2 nights
Clonakilty 1 night
Dingle 2 nights
Doolin 2 nights
Galway 1 night (maybe, but might also stay in Doolin and forego Galway this visit)

Still multi locations stays but I feel the above allows us more time to see the things in Dingle/Doolin yet also give hubby his music fix and spend a little less time scrambling around. Still a lot in a week, we know that for sure, but I feel a little less pressure.

Another question: Since hubby's birthday is now going to be spent in Doolin, I found recommendations for two restaurants: Homestead Cottage and Oar Restaurant. Thoughts on one over the other? Also, any suggestions for accommodations in Dingle and Doolin?

Thanks, you've all been so helpful!!