@FlipFlops4Me I really feel for you and your DH. Sadly inheritance and money can make people act completely out of character. I agree that kind of money in your 30s shouldn’t be seen as not enough as it’s a great deposit for a home.
You are not doing anything wrong, as an executor you need to follow the will and do your best for both beneficiaries.
The will stated to sell the house, which is what you are planning to do. This is following your MIL wishes, and is definitely in the best interests of your DH but also for your DS, even if he doesn’t realise it. Being a landlord is not a get quick option there is a lot of responsibilities and hidden costs.
As pp have said I think your DS will struggle to buy out your share e.g. getting a buy to let mortgage. I also think he may be unprepared for the true cost of being a landlord.
I know this may delay things but let the dust settle and then talk to your DS again. Reiterate your MILs will shares the estate 50:50 and your DH is entitled to his 50% to make his life as comfortable as possible. Make it clear this is non-negotiable as your DS does not have the right to dictate what DH does with his inheritance.
Point out that if your DH (or you) need care in the future the LA would see the property as an asset to be sold to fund care.
Then set your DS a task. If the house is c£285 (get 3 current valuations) and c£85 in cash your DH is due to inherit c£185. As there is c£85 in cash DS could give this all to DH and would then only have to raise c£100k to buy your DH out of the property.
Tell your DS to get an offer in principle for a c£100k buy to let mortgage. Ask him to also produce a fully costed plan for letting out the property including cost of getting it ready to let, maintenance, advertising, legal requirements, empty periods between let’s, tax, insurance, CGT etc. He also needs to think through the unthinkable e.g. what happens if he or his DW become injured, disabled or die. Then you will talk again.
I suspect once your DS actually starts to look at buy to let mortgages and the costs of renting the property out he may realise it’s not as easy or lucrative as he thinks.
Give DS a timeline to do all this e.g. property goes on the market 1st January 2023, it will focus his mind.
In the meantime get quotes for the work to be done on your home and also find an Estate agent. It will take time to realise the cash from the property so getting an idea of the cost means you are able to move quickly.