I'm sorry things are so stressful and I'm sorry about your mum - I'm sure she would pause the repayments to her if she could.
I agree with most others that I wouldn't sell up to step off the property ladder - only to buy cheaper if you decide to do that.
You have a mortgage free house except for this 50k loan - which you are not charged interest on. You won't be in a stronger position other than "downsizing" to cheaper.
I would also urge you to speak to Stepchange or CAP (Christians against poverty) or national debt line.
They can help you draw up a budget and decide what you can afford to pay creditors. So for example the loan you are paying. You might be paying £250 but find you can offer them £40 for example. You are supposed to offer all of your creditors in fair proportion to what you owe and can afford.
With poor credit and no need for a mortgage you don't have to worry about your credit rating if you default on loans.
Ask for advice about the loan to your mum as well. I think the theory is if you offer what you can afford to pay then even if it went to court you would only be asked to pay what you can afford anyway. Your mum wouldn't want you to lose your home to pay this. I know it isn't her choice now but the local authority are not going to quickly act to boot you out of your home if payments reduce while you are between jobs. Those wheels would grind very slowly.
The Debt Free Wannabe section of the Money Saving Expert website has a lot of people who are very knowledgeable about your rights managing debt.
I think you need to be more open minded in your job search. You could teach outside of your specialism (some subjects struggle to recruit specialists) or get a job in a different sector.
If you could get an evening and weekend job in a supermarket or hospitality you could keep your days free for supply teaching - and if you think you will only get two days supply that shouldn't be too much.
Doing supply is good because it's getting your face know in lots of schools if jobs or longer term supply come up.
Strip it back and you are mortgage free and in uncertain work. Due to the fact that you are mortgage free any work should tide you over in the very short term. You would claim universal credit if your income is low and default on your loans and debts for a while if you have to.
You describe paying off utility debt from £2000 down to £300. If you are paying it off at £100 a month (might be more like £150 from the sound of your bills) that debt will be gone in the next three months.
Like most of us you feel you need to pay all your obligations but you might need to learn about and adopt a new attitude where you know what your priority bills are and what you cannot afford to pay doesn't get paid for a while. It's scary if you have never not paid loans and debts but it is officially a "thing". That's why unsecured credit is more expensive- it's risky for the lender. You prove what you can afford and pay it and then generally lenders don't bother to take you to court as even if they did they wouldn't get more.
You can do this x