I am confused here. Early in the thread
@JamesMcyntyre you said you had paid the fees, in relation to the power of attorney. You only pay when you register it. Has a POA actually been registered with the Office of the Public Guardian? I will assume that it has not been registered.
If as
@canary points out, your mother no longer has capacity to sign a new POA, and you cannot get agreement on completion of the draft POA if it hasn't been registered, then deputyship is the way to go.
Now, if the POA has not been registered your sister can only access your mother's money with her permission. She may have that permission. Or she may have stolen money. We don't know and retrospective proof as to who agreed to what is very unlikely to be available.
So, for the future you could apply for deputyship with you as the only deputy. You could make the case in your application that your mother was at risk of depriving herself of funds by giving money away to your sister over and above reasonable expenses. If granted, this would put you in full control. You would be able to change passwords, cancel or replace cards, have all correspondence sent to you. You would have to account for all spending but you could pay your sister a shopping allowance for domestic expenses and food etc. Anything your sister wanted to use your mum's funds for would have to be for your mum's benefit and authorised by you.
This would be the best thing for your mother but will obviously be a source of strife and your sister may object to you getting deputyship. But she may not, as she may not want her past misuse of mum's funds to be put under a spotlight. You could make the point that bygones will be bygones and that provided she doesn't try to prevent you from becoming deputy, issues such as using a car without the owner's permission, misuse of mother's funds, etc. will never ever be spoken of again.
In the circumstances I would suggest having a solicitor on board to advise or do the application.