She who? OP? She doesn't have the "authority." Sister with POA? She won't even hire/consider respite for sister, not likely she's going to consider moving mom... She's got a good racket going - let sis care for mom, and save all the assets for ME!
Is your mother competent to hire and pay for her own care needs? Unless, she has dementia or is not able to manage her own affairs, with help, of course, then, the POA has no authority to act on her behalf, UNLESS she tells her to. If mother is incompetent, I'd consult with an attorney about the options of filing for Guardianship or having you appointed POA, if mom is still competent to to do it. When someone is of advanced age, changes like that are suspect. It might also help to obtain an assessment of what mom's needs are, so, the costs are justified on paper.
Tell your sister, I am willing to do X, Y and Z and no more. Mom needs more help than that, and I will call APS if more help is not provided, and state will take over
Just remember that the state is not always good at investigating financial exploitation and stay on the investigator and learn at the beginning who her supervisor is. Keep written records of everything that happens.