As POA you have the RESPONSIBILITY to not only monitor, but to CONTROL (conduct, manage, and protect) your mother's affairs if you have reason to believe that she is not capable of managing alone. If she has been diagnosed with dementia, a letter from a doctor is sufficient proof.
It is not clear to me why your sister needs to be on the account with your mother, unless she is the primary caregiver and lives with her. Even IF that is the case, she may not necessarily have the right to spend your mother's assets without your permission and oversight - preferably IN WRITING, and with CLEARLY DEFINED PARAMETERS.
By the same token, if your sister IS in fact the live-in caregiver, you need to understand the thankless nature of the job and not unduly withhold funds, so that your mother and sister can live comfortably together, INCLUDING providing for RESPITE breaks for your sister.
In order to make all this work out so that your mom does not run out of money, you will probably need some help with budgeting and long-term planning. You can best get this by hiring an estate attorney with a specialty in elder law.
If for some reason you are suspicious of your sister's having been added to your mother's account(s) you can ask yourself (not your mother - yourself) these questions.
"WOULD MY MOTHER HAVE PUT MY SISTER ON HER BANK ACCOUNT OF HER OWN ACCORD?"
"WOULD MY MOTHER HAVE GONE TO THE BANK AND MADE THIS CHANGE IF MY SISTER HAD NOT TAKEN HER THERE AND ENCOURAGED HER TO DO IT? "
If the answer to either of the questions above is NO, then your sister would be considered to have exercised "UNDUE INFLUENCE" over your mother. In every state, if your mother is over the age of 65, this exercise of undue influence is considered a crime...
Presumably, your mother gave POWER OF ATTORNEY to YOU before your sister was added to your mom's account. Therefore, one would assume that at the time your mother made you her POA, she was mentally clearer than she is now, as well as when your sister "was added" to the account.
POA is a tough job. It can make for a lot of resentment. But done well, it can REALLY make the difference between a disaster and a happy ending for a vulnerable elder.
KEEP IN MIND your mother has given YOU the power to PROTECT, to CONTROL, and to MANAGE - her affairs. In order to do it, you NEED to have DETERMINATION, and COURAGE...
But remember: *You ALREADY HAVE the POWER!!" (Literally)
Hope this helps.