Appreciate advice on itinerary (with kids)!

I've never been to Ireland so I can't comment on your itinerary, BUT - be aware of car seat laws, as they are a lot more strict than in the US. My kids are 11 and 9 and out of car seats - but would be required to use them in Ireland. Here's the website: https://www2.hse.ie/babies-children/child-safety/transport/car-seats-and-child-safety-cars/#:~:text=By%20law%2C%20a%20child%20must,weigh%20less%20than%2036kg%20(79lbs)

Don't let this deter you! Just something to be aware of, especially since you are planning to rent a car.

Rather than book Killarney and Dingle separately, consider just stopping in one place and do everything from there.... Each time you change location eats into time. Two nights only effectively gives a day and a bit to explore the area. I night even less. From your list you need to allow at least 4 nights for Killarney/Dingle areas as there is so much to see and do around there.

Travelling to Galway will take up virtually the full day especially if driving via Doolin and the Burren. This means just over two days for Galway . The Aran trip and Connemara day trip will use up both of those full days.

"Rather than book Killarney and Dingle separately, consider just stopping in one place and do everything from there"

That would be my suggestion too. After a much regretted first stay in Killarney town many years ago we've subsequently elected to find accommodations somewhere between Glenbeigh and Castlemaine - far away from the congestion of Dingle and Killarney yet convenient for easy day trips to visit both. Would simplify your logistics to unpack once and be done with it for several days rather than having to constantly relocate.
You'd also be close to the Gap of Dunloe - one of the prettiest little glens in Ireland - from where you could hire a pony trap for the ride up to the head of the glen and back - about 7 miles round trip.
If the weather cooperates, driving north via the Tarbert ferry is something the kids might enjoy. There's a very nice (but easy) cliff walk at Kilkee that we always enjoy, and the little town with its pretty stretch of sandy beach is a nice stop for lunch or a cup of coffee. Heading up the coast along the N67 towards Doolin will take most of the day allowing for stops along the way, of which there are plenty - it's one of Ireland's great scenic drives on a sunny day.
Might add that April is our favorite month to visit Ireland. The flowers of early Spring make any excursion out into the countryside a festival of color - the country is basically one giant garden that time of year. Be prepared though for the occasional "all 4 seasons in one day" experience if a shower rolls in off the Atlantic. They typically pass pretty quickly however.

Thanks, Allison, good info! And Robert and wasleys, thanks for the advice! I'll take a look at options for one spot for all three nights. Excited to visit in April!

Any advice on towns in the Burren that would be good to explore? Doolin? Thanks!

I understand your desire to minimize the number of places you stay over but to me it seems inefficient to stop in Doolin on the way to Galway and then return to Doolin from Galway for the Cliffs of Moher. I stayed in Doolin a couple nights, hiked the Cliffs of Hoher cliff walk, and took one of the Doolin ferries to the Aran islands. You can also see the cliffs from the water while in Doolin.

f you are interesed in trad music, Doolin in the evening is great for that. People bring families with kids to the Doolin bars best know for the music.

I think CD in DC, the OP is intending to do a boat trip to the Arran Islands and Cliffs of Moher from Galway. They won't be travelling back to Doolin from Galway...

Use the Tarbert to Kilimer Ferry as Robert suggests. The Burren covers a big area and with its limnestone scenery is completely different to anywhere else in Ireland. With just a day to do the drive, you will have to be selective as to what to see. There is basically two choice of doing places like Ennistymon with its stream and rapids and Kilfenora with its cathedral and carved crosse, driving up through the centre of the Burren. Alternatively you can take the road along the coast from Doolin through Fanore and Murroogh to Black Head and then round to Ballyvaugh and Kinvarra (Dunguaire Castle).

@ wasleys, yes, thank you! Does the ferry save time as well as add interest? Thanks for the town suggestions! I'll take a look.

I realize I may need to scale back my ambitions a bit, especially during the end of the trip (and the kids might be tired of hiking anyhow). We might miss Connemara to allow more time for Galway (I studied there, so I'm eager to have a day around town).

Thank you all for the advice, much appreciated!

The ferry route is slightly shorter than going round by Limerick - whether its quicker may depend on how long you have to wait for a ferry...

Don't completely miss Connemara. Even half a day driving to the small town of Roundstone with its harbour (and possibly one of the best views in Ireland) and then to Clifden for the Sky Road. On a good sunny day, this must rank as one of the best short drives in the world.

Actually, I think the coastal route via the Tarbert ferry is the long way around - really only suitable if you're up for an all day meander with numerous stops along the way.
If you just want to get to the Burren as quickly as possible then the motorway from Limerick will be the much faster (though far less scenic) way to go.
I second all of wasleys suggestions re Connemara - it's all great. Would only add a possible short ferry trip from the village of Cleggan over to the island of Inishbofin - one of Ireland's better kept secrets IMO. The ferry ride is barely 20 minutes and once on the island there are pretty little (level) walking paths along the shore in both directions ... one of which leads to the ruins of an old church that the kids might enjoy exploring.

Thank you, both! Super helpful.