If your mum is taking out cash and you can't stop her but she's hoarding it at home then that's not the end of the world - it's still in her possession, she's not being scammed. Hopefully you'll be able to find it this afternoon.
If so the question is what to do next - think carefully, the best thing might be to do nothing in the immediate term, especially if she is deteriorating and you can see a time ahead where you will be able to take control without a massive row.
Regarding capacity, the question is does she understand the ramifications of taking out cash and doing whatever it is she is doing with it? (Does she know she has dementia?). It's always a bit of a nightmare, the capacity thing, and clearly she's not going to voluntarily give you Finance POA.
I can't see that there are any tax implications; inheritance tax only applies to what is actually inherited so if she's thrown the money in the bin you won't inherit it. Care home fees - if the council consider she has been deliberately depriving herself of her assets to avoid paying for the care she knows she's going to need then there might be an issue with funded care. But as she has dementia and as the money may well be stashed somewhere at home then that's not going to be a problem either.
So my advice would be - don't panic, and don't rock the boat or you may find yourselves even more shut out. Try to find the money - hopefully it's in small notes so less hard to find. Talk to the bank. And join a Dementia Cafe/online support group/carers group/whatever, you'll find a wealth of practical information from other people who've been through it like you have.
Good luck, it's such a tough thing to be going through.