I think BethFL's minimum lengths of stay are extremely reasonable for traditional tourists with limited time. From reading your previous itineraries, I don't know that you are so traditional in your interests, and I remember that you are able to take longer trips, so I'd be inclined to add some time in London.
The places Beth lists are among the most expensive in the UK. Other costly destinations are Oxford, Portree on Skye, Oban and coastal towns in Cornwall that are accessible by public transportation. I know you generally rent a car for at least part of each trip, so staying in towns not on easy public-transportation routes will probably help considerably.
Cities I've visited since 2017 that were a lot cheaper than London, Edinburgh, etc., include Brighton, Norwich, Liverpool, Glasgow and Dundee. All were very appealing to me, but they're only recommendable if they fit your interests. There's a youthful liveliness about Brighton and Liverpool that the teenagers might find appealing.
I'm sure you can find something affordable that will allow visiting northern Wales by car. I based in Chester but don't remember how my lodging rate there stacked up.
One suggestion I have is that you not pay London lodging rates while daytripping to multiple sights well outside the city.