Option 4 is to downsize and compromise. So the kids share a room, you go from semi or detached to terraced, you lose the garage, you have a smaller garden.
Personally, space is crucial for me, so I would move somewhere cheaper.
You definitely need to do a reccy and get on the road as much as possible, we have looked at several places that look good on paper but just ‘feel’ awful when you get there in person.
I know nothing about Newcastle except the coast up there is meant to be lovely.
Most of North Yorkshire does not have big towns or cities, those that do aren’t massively affordable. 400k in Harrogate will buy you something of a half decent size but you will probably have a yard instead of a garden and no parking (I have a huge aversion to new builds, idk what those are like in the area).
We almost bought on the outskirts of Middlesbrough due to house prices two years ago. I didn’t feel happy driving through there and four separate people have since pulled faces at me when I told them I almost moved to Middlesbrough. It’s one of those places that is regularly listed as one of the cheapest places in the country to live… for a reason? Idk. We didn’t really spend that much time there. Those reactions were a bit disturbing, I feel like we dodged a bullet. I have noticed prices are now going up there, presumably because everyone has heard how cheap it is, and the North is running out of big towns that are also affordable.
You could consider Carlisle where prices are still reasonable. And County Durham: Darlington is a big town that has a lot of government offices moving there, Bishop Auckland is meant to be a bit run down but it does actually have shops and is REALLY reasonable for house prices. These are not ‘naice’ places in MN terms, they are liveable places because they have amenities. I quite like County Durham. Lots of pretty hills and castles and a bit of Moors, and quaint villages like Barnard Castle. The castle near Staindrop has deer running free in the grounds! Middleton St George just outside Darlington seems to often have reasonably priced family sized homes. Never been there though. Check what’s happening with the nearby airport if noise is a consideration.
Sorry I can’t help a jot re: schools.
Your OH should look at Scottish taxes before continuing to flirt with that idea. Also, the council tax bands in some places seem really harsh, e.g. a band G for a 1450 sq for, 3 bed flat (in Peebles, a desirable village, apparently). Scots also pay more for petrol and electricity.
Once you have made a decision, if it’s an area switch you decide on, pop a post in Property/DIY to narrow down options on some places.
We spent a lot of time looking at N Yorks. 2 years, in fact. Feel free to pop me a message with questions on any places you have in mind as long as it doesn’t pertain to schooling.