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A living Will is usually set up in order to take care of this exact situation. It selects the individuals responsible for financials as well as medical care. It seems that you have a very limited Power of Attorney and your sister may have a more general one. One of you probably has Power of Attorney over all the bank accounts and more likely than not, your sister knows where the money is going since she has control over it so you should ask her.
Medicare probably does not have control over your mom's finances.