So sorry to hear you're in this situation OP. I think you need two sorts of advice.
Housing advice, regarding your housing situation, and benefit advice. Macmillan will be able to help you claim PIP, and probably give you advice re other benefits too.
With your diagnosis, and if your disabled son is going to remain living with you, you may be eligible for council housing. Ring the council and ask to speak to someone about homelessness, explain that you're a carer for your disabled son and that you have a terminal illness.
Another possibility is using your share of the equity in the house to buy part of a shared ownership property and then you could get UC to cover the rental part.
If you're intending to use the money from the sale of the matrimonial home towards a new home, it will be disregarded for benefit purposes for (iirc) at least 6 months, so you could still get UC while you find a shared ownership place.
Your son will soon be able to get UC in his own right, and will hopefully get the extra £354 for limited capability for work related activity once he's been assessed, plus his PIP, so he should be able to make a significant contribution to housing costs, bills and food.
If the area where you're currently living has high house prices, your share could be enough to buy in a cheaper part of the country if you were prepared to move to a different area. A friend has just moved to Shropshire from Sussex for exactly this reason.
I'm gobsmacked by the divorce settlement though. That's brutal.