I really feel for you! And so sorry you're feeling so isolated and down.
Benefits wise - possibly Carer's Allowance for your wife? Her earnings would have to be no more than £116/week, so depends on how much she earns from her part-time job...
I'm sure your family don't feel pressurised by your situation - maybe have a chat with your wife about how you feel. Possibly getting budgeting advice could help with the cashflow, there are bound to be services locally who could help with that? Also there might be ways you could help while stuck at home that could help you feel like you're making a positive impact... https://www.moneyadviceservice.org.uk/en/categories/cutting-costs
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