HI OP,
Cornwall is beautiful. I lived there for several years and the main reasons we had to move were work and distance from family when we had our first child. If my family lived there I would love to move back.
I think your finances would be much more manageable if you are able to work also. I think a family with a child on only your husbands wage would probably be entitled to some universal credit which you could see by looking at https://www.entitledto.co.uk/ Although I don't know if you are entitled to benefits for a while having lived abroad?
The MSE calculator suggest 150K mortgage at 5% will cost you £877 a month over 25 years. https://www.moneysavingexpert.com/mortgages/mortgage-rate-calculator/ That's a £300k house with your 150K deposit. That's a possible but modest house in Cornwall. £200,000 for a £350K house would cost you £1170.
Does your partner have a job paying 37K lined up or is your OP based on them being able to find a job earning what they earn now? Moving hoping to get a similar paid job is a very risky strategy in this low wage part of the country.
Similarly for you if you are a teacher/TA/school office - you should get a job in time but are you happy to work in a hotel/supermarket/fast food restaurant while you find something in your field? If you are then you should be able to find work quickly, if not it might take you a while.
Will you still have your 150K deposit if you have to rent for a year or two? A rental house can be very hard to come by. You might have more luck with renting a little flat but that might not be what you had in mind. Sometimes working people are having to live in temporary accommodation/holiday parks as they can't find accommodation (which is a scandal when there are so many empty houses but that's for another thread). If you have the option to live with family until you buy that would save you a fortune (even if you compensate them) and be less stressful than trying to find a rental.
Have you got separate savings for surveys/solicitors/stamp duty. Take a look at the Government stamp duty calculator. The stamp duty is higher if you have been non resident at £17.5K for a £300k house versus £11.5k.
On the upsides Cornwall is beautiful and I found the people (who seemed to be about 50:50 Cornish versus movers) to be friendly. Some people will say that they hate the busy summer months with holiday makers and owners of empty homes are not likely to be made welcome.
Overall I think you can live a great life with less money than many parts of the UK as if Cornwall suits you you don't need a budget for holidays away - you can get to (what feels like although I haven't counted) 100 beautiful beaches within an hour. You can walk endless miles of coastal paths, you can paddle, swim, surf - whatever floats your boat.
I don't think there is as much need to "keep up with the Jones'" as there might be in other places. A comfortable home (in the literal sense), a car that gets you from A-B (or the house to the sea) and enough money to pay your bills and get your life basics and you have everything you need in Cornwall in my opinion.
Downsides are that teenagers might find it tricky if you are in an isolated part rather than for example Newquay and ask for lots of lifts or the dreaded scooter. In the future your child might find it difficult to find work that pays enough to buy a house and need to move away or decide not to return after uni. If they stay in Cornwall/don't go to Uni there is a high chance that they could be low earners/seasonal earners.