There are some parts of your posts which really do show how bad things are-
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Those children really are a credit to your sister but would your Mum want them to become unpaid carers?
Then there's this; your Dad telling you that he can't cope and that statement alone should be telling you that you NEED to be looking at care homes.
Money yes, it's always an issue but once your Mum's funds fall below the limit, SS will step in.
And it's fantastic how your family have pulled together but with your Dad's additional needs, I doubt that this is sustainable long term.
You and your family really are a credit to your parents but now there are difficult decisions to be made.