@Snorfig I’m so sorry to hear about how things are. PPs have given good advice above, but I suppose I just wanted to add a point about whether you can increase the amount of money coming in, as that may enable you to outsource some of the humdrum daily stuff (like reinstating your cleaner), or help buy in more support / time away from dc? Are you in UK?
I am not an expert on benefits - but have you checked you are receiving everything you may be entitled to (esp with regards your dc)? Are you receiving any form of child maintenance?
Have you considered your employment - you mention you are in a high pressure role in the public sector - can you weigh up the pros and cons of possibly moving to a similar (if possible) role in the private sector? Might the remuneration be better?
One other thing that occurs to me is it sounds like you are experiencing burn-out, particularly to do with your caring responsibilities. If work is something you enjoy and find fulfilling, then have you considered the pros and cons of increasing the amount of time that you work?
It would potentially improve the financial situation, allowing you to out-source some things, but may also give you a better work-life balance. I was a SAHP for a while (we have SEN dc), and there may sometimes be a benefit for the dc if they get a bit less time with the parent, but the time they do have is much better quality time as the parent is not so burnt-out from focussing on (what sometimes feels like) the relentless needs of dc.
I find that if I attempt to do the cleaning, it is never limited to 4 hours, it will take me longer as I hate it and find it soul destroying. Maybe increasing your paid work (even just for a half-day a week) may pay for a cleaner, plus a while host of other things), and shift the balance of your week slightly, so that you are spending that extra half day (at work) doing something where you feel fulfilled and valued.
Can you slot in more endurance exercise into your day (if that really helps you cope)? Some people I know have switched from commuting by tube / train to running to work (often workplaces have showers), or cycling?