My sister is POA of my mom's healthcare and made false accusations against me concerning mom's healthcare. Can I fight this?

This is heartbreaking - and unfortunately not all that uncommon. Contact an elder law attorney to see what your rights are. You can contact your state law association to see if anyone would take this "pro bono" or free. Good luck,
Carol

Of course. Hire an elder attorney. I am sorry you are having to deal with this...