welcome to TP
sounds a bit worrying maybe
just to be clear, though - you've checked that the payments aren't being used to fund home care visits, day care etc for your mum, or you can tell that your mum's care is being paid for and this sum is over and above those payments - the sum you mention would work out at about £36 a day, which isn't substantial as care fees go
if the care fees are being paid, and the sum you mention is additional, then £36 a day does seem a lot - however, if your sister takes your mother out regularly, buys incontinence supplies, does her everyday shopping, and pays for the type of extras she mentioned .... the total does begin to add up - are there large amounts going out of the account at irregular times or small amounts often; might give you a clue as to where the money is going
do think that you have left your sister in charge for quite a few years without you all sitting down to go over the finances, so even if she has done nothing untoward, she may feel upset that you are questioning her now - if she has been taking out too much, at least she now knows that you all will be checking future accounts together
does anyone have Power of Attorney over your mum's affairs? if not, and if your mum still has the capacity, best get these in place (go for at least 2 Attorneys to act jointly and severally, with maybe a named replacement as well) - if your mum no longer has capacity, then someone needs to apply for Deputyship - strictly legally, no-one should be managing your mum's affairs without legal authority, and definitely not without her express permission - banks are not happy with another person having someone else's card, knowing the PIN and using it; for good reason - indeed, should the bank believe that your mum no longer has capacity to deal with her finances herself, they have the authority to freeze her accounts until someone shows they have the legal responsibility to manage the money for your mum
maybe all of you could sit down and agree what to do for the future and how you will oversee your mum's finances
best wishes