It can be hard to think clearly when you are bogged down with multiple issues.
Get some experts in for advice about a proper loft conversion - see if it is possible and the likely cost.
Speak to your bank about remortgaging to free up cash to pay for it. It costs nothing to ask.
Speak to your local council for advice. Due to your daughter's medical needs and the simple fact that your family has outgrown your house you may be eligible to go on the council waiting list or for a home improvement grant. Homeowners like yourself can go on the housing list if they live in an unsuitable or overcrowded property and can't improve the conditions.
Also, look at private rentals in your area - the rent may be affordable especially if you have equity in your property. You say you can't afford private rent but just check out what is available. Rent might be cheaper if you are prepared to move further away.
Speak to a few housing associations.
In the meantime is there room in your bedroom for your son's bed? Not ideal but he might get a better night's sleep and your daughter will have her privacy. A good quality bed settee in the living room for you and your wife is an excellent suggestion. Many families live with this arrangement when there aren't enough bedrooms to go around.
Make a list of people to talk to and make a start on Monday. You will feel much better if you are taking action.
Regarding your partner. Could she think about taking on any sort of work short term until her ideal job comes up? For example, Amazon offers drivers the option of working hours that suit them, even three hours a week delivering parcels.
https://flex.amazon.co.uk/
It is always easier to find employment when you are working.