Unfortunately people who haven’t had to undertake the role themselves or don’t have close relatives undertaking the unpaid carer role they have no idea what it actually entails. They don’t understand the daily grind on a never ending hamster wheel - same routine everyday and no respite because the social service offering is inadequate - regardless of what they are supposed to provide.
If there is cognitive impairment it’s even worse as it’s difficult to feel if the caree understands and can communicate , making life very lonely. Physical disabilities mean manual lifting / handling - it’s hard graft.
Everything is a struggle to get the right support and the never ending hospital visits etc. Money is tight because the unpaid carers allowance is minimal and to be eligible you can’t earn more than a penny over £151 after tax it get deducted. Kiss goodbye to any respite unless you can pay for it yourself. While you do it for one you love - a DP or DC it’s not something everyone is cut out for and it’s bloody soul destroying, stress inducing with depression and anxiety are also high on the list. You can’t go home at the end of your shift either because it’s 24 x 7. Try looking after someone when you are ill yourself, you can’t just take a couple of hours out because you have a headache, or toothache or worse - you have to plough on.
Not everyone is cut out to do it ( and it’s a shame in this country we don’t recognise caring as a valued profession, because it is ) and there is no problem in you being honest with your sibling and telling them you won’t be able to help.
While I’m sure the suggestion is meant with the best of intentions I suspect they don’t really understand what it will mean in real terms and the impact it will have on their daily life. Perhaps you could share some of these posts with your sibling to make sure they really understand what it will mean when you sit down to talk to them. From your description it sounds like you would both be better putting your efforts into finding a suitable care environment. If they have less than £23,500 or so in savings LA support should be available to cover costs.
Good luck with your chat , but for your own sake, family and sanity stick to your guns.