2 week itinerary feedback - Northern Ireland + West Ireland

For political history, the Museum of Free Derry and the Bogside Murals make an interesting counterpoint to the Black Cab Tour in Belfast (although 8 might be a bit young for the latter). You're right that staying in Derry with a car can be a challenge (although there is parking at the mall). I've seen a recommendation for Letterkenny as a place to stay, but with a car, just set the map wide and see what you find. I also found Derry accommodations a bit expensive.
In Donegal, I really liked Killybegs, which gives access to the Slieve League from both land and sea. I can recommend an excellent AirBnB there. Same with Sligo, actually.
The kids will be allowed in the pub until 8 or 9pm. Music wouldn't generally start before that except on Sunday unless there is a music school or festival in town.
Maybe think about staying near the "family history sightseeing," wherever that is.
I'm not sure how many swimming pools you'll find in Ireland. Wild swimming is popular, though.

Thanks, @G3rryCee! Please feel free to recommend specific Airbnbs in Killybegs and Sligo! And thanks for the suggestion on what to do in Derry and the prices.

We're headed that way in a few months and I decided to make Derry a day trip from Letterkenny, Not only are the prices and parking better, but there happens to be a regular trad session at Blakes on one of the days we're there (Monday).

If you want to visit a group of Neolithic cairns/tombs where you'll likely be the only one there, try Carrowkeel Tombs on the way to Sligo. Easy hiking on a farm road, then a short climb up a rocky hill to a group of mini-Newgrange structures. Not well signed, and you can drive farther up the road past the gate to a large turnout. I would have enjoyed it as a kid. We were there in May and met one couple along the hike.

I sent you a private message. I forgot to mention that the Sligo place might only have street parking, but it looked ample. We didn't have a car, so I didn't pay a lot of attention.

remember you now need a ETA to enter the UK (Northern Ireland) www.gov.uk/eta
also please check if you can take the car from Ireland to the UK (Northern Ireland)
the UK like the US drives in MPH, were Ireland drives in KPH, also please please read the highway code for the UK i have posted below this is for your own safety road signage and markings are different in the UK compared to Ireland
https://www.nidirect.gov.uk/articles/highway-code

We stayed in Coleraine one night enroute to Derry vs (in Derry) at the Ibis. We were traveling opposite direction. It was very much like stopping "off an exit," but super convenient (gas , shopping). We were able to do all of our grocery shopping etc. The hotel was quiet, clean and reasonable. It also included a hearty breakfast which increased its "value" and reminded me of a Hilton "Tru" property.

We only spent a day in Derry -- walked the walls and had tickets to the Derry girls exhibit at the museum. Our detour was to Grainan Allech (spelling??) -- also worth it. Lovely views.

We stayed in an airbnb in Donegal (town), called Riverview house. Probably bigger than you need but also recommend