Itinerary Suggestions with Kids: Feel Overwhelmed

I highly recommend taking a tour at the Kilmainham Gaol in Dublin. It will give you and the kids a great history lesson, and make everything else that you’ll see later make more sense.

Agree with the suggestion of the jail.

For kids, I highly, highly recommend Blarney Castle. The grounds are wonderful for kids to explore. There's a fairy glen with a wee house, a witch rock, and more.

Apologies but digging more in wondering if the below is more ideal? This cuts out the drive more North to Galway and Conemarra in exchange for additional time in the Cork area.

2 nights Dublin
2 nights Cork
3 nights Killarney (use one day Park/jaunting and another Dingle)
2 nights Lahinch (Burnatty Castle and Cliffs of Moher)

First, definitely fly into Dublin and out of Shannon (or vice versa). You might be able to keep Cork to one day if you stop at the Rock of Cashel to or from Dublin and the west. And if the reason for Cork is the wildlife park you could substitute the Dublin zoo and use your Cork days somewhere else. I don't know anything about the wildlife park so may be that's not a reasonable substitution. I have heard that the zoo is very good. The drive from Killarney and then clear around the Dingle Peninsula and back to Killarney would be a very long car day. The Ring of Kerry would be much less driving and if you spent a day at Killarney National Park you wouldn't even need to do the entire Ring of Kerry since part of the Ring is the park.

Killarney is great fun, but extremely touristy and super busy. When we go back, we plan to avoid Killarney and do Kinsale

i agree with fly into Dublin and out of Shannon. makes things much easier. The driving is a lot. when i went recently (with no kids) we originally planned to finish by going up to Galway, but another day of 3 hrs of driving was just too much. So went to Dingle instead and loved it. Changed plans while we were there!
Dingle is nice because it's a cute town that's fun to walk around in, and there are lots of ice cream places.
With little kids i think you would want to minimize changing locations. i would try to stick to 3, not 4

So many potential choices. Just deciding on which would be best/entertaining for kids.

Dublin to Killarney to Galway

Or

Dublin to Cork to Killarney to Lahinch area.

The four changes doesn’t bother us (just did 8 days in Colorado with 5 changes and kids aced it). I tend to think the second one to give access to Fota, Blarney, Cahir and donkey is best but lure of wanting to see Galway keeps me torn.