Could you get her to sign a short note, dated, saying she gives you permission to use her credit card to pay for household essentials and maintenance, in this case the plumber? If she can't or won't or both, then I would use it, but keep STRICT notes of what you did, and why, and when, and of course...
Yes, ideally, get mum moved to a ground floor easy access flat, that is in a joint tenancy with your brother, so he can't lose it when she dies/goes into a home. It's really important to sort this out now (because it will probably take ages for a good flat to come up for her!) Dementia of any kind i...
Is your brother on the tenancy of your mum's flat? If not, he will be made homeless if she has to go into care? Or when she dies, whichever is soonest.

This is THE most important question right now!
If you're not in a union, join one straight away! They are 'on your side'. No one else is.....(and HR is DEFINITELY not on your side - don't trust them an inch!)
In haste for now - you can't go on like this. You are daydreaming of 'escape' and this is SO typical when someone reaches the end of their tether, as you have. You have 'sustained stress' for years and years. It's sad re your FIL, but please don't worry about him - dementia brings its own 'protectio...
She'd be exactly the same in any care home she moved to - so don't move her if this one is good. Talk to the staff there - what is she like when you are not there? Like toddlers etc, our parents are different with us usually than they are with 'teachers' (ie, staff), and they may well paint a quite ...
Tell your local press. Local newspapers like local stories and it might 'kick' the useless SS into action.

Also, yes, stir up legal action as well.

Or maybe just take your poor dad to A&E and leave him there, making sure there are NO housekeys on him so they CANNOT return him home.....
Paul - his problem. Not yours.

Stay out of it!¬!!!!!!!
It seems bitterly ironic that it is the very government department that is set up to SUPPORT you, that is making life difficult! I can't give you answers, only sympathy right now, but I know there are plenty of folk here on the forum who know the ins and outs of getting financial support and so on, ...