Ireland/Scotland- Spring Time

I can't speak to Scotland, but 8 days is going to be tough to tackle ROI (I have no idea about Northern Ireland, which is part of the UK) with kids and a woman (meaning you can't move as fast as you want.) You can drive from one side of Ireland to the other in an afternoon, though. However, just because you see a road leading to a site you want to visit, doesn't mean it won't shrink down to 2 inches wider than the size of your car, or be full of sheep, or be curvy as hell (slowing your travel times.) Driving in ROI is easy, just get the smallest car you can.

I've always flown into Shannon (SNN), so consider that too. They have a CBP pre-clearance facility there, so the return is always a breeze. The military used Shannon to get Joes and Janes overseas. Shannon is also closer to most of the stuff you likely have on your list (Ring of Kerry, Cliffs of Moher, Kylemore Abbey, etc.) There are also ferries between both Northern Ireland and ROI and Scotland/Wales.

Your biggest problem is going to be the weather. Tourist season starts the last week of May for a reason. You will 100% need rain gear. Bring good shoes that have traction on them, because a lot of stuff you'll be visiting will be made of stone of varying levels of slipperiness when wet. You will learn the love the smell of peat fires anytime you're in a pub eating with family.

Blarney was clearly a check box only for me, but now I can't shut up, so maybe it worked? That was when I started noticing where the toilets were in towers, and I developed a small obsession with noting how high up people would stick their bare rear ends over the ground.

The Rock of Cashel was more impressive due to the military strategy of its placement. The structure itself was pretty broken down by comparison, but when you see the view you get in all directions, it was a perfect place to build a fortification (ignoring supply needs, of course.)

During tourist season, the Ring of Kerry is packed, but OP isn't going during tourist season. Hotels are 1/2 price outside of the high season, too.

Cahir castle was totally complete. It was surrended to Cromwell without damage so it's totally in tact. Of all castles it was my favorite. Thirty minutes from Cashel. I stayed a block away in Cahir house m highly recommend.

You will be hard pressed to see either country in only 8 days but that is at least doable. In my humble opion there is no way to see both countries in 8 days. And I would agree with Dingle and Galway and add in Killarney. The music in the pubs in Galway is a blast..

I regret not getting to Killarney. It rained bad that day so we headed towards Limerick instead and it sucked there. Regretted not staying an extra day in Dingle.
We also texted a place in a "castle" outside Galway but it was so bad even though we prebooked two nights we left the first night. It wasnt fit for habitation Sadly.
Learned to drive in the pitch black in the rain the wrong way on a one lane road with lorries. Great times.

I would not try to do both countries on the same trip.