How can I get POA over my sister?

No one can "get POA over" someone else.  A power of attorney can be granted by the person who wants someone else to also be able to make financial decisions (a Durable Power of Attorney) or to speak for them, communicating their choices, when they cannot communicate (a Medical Power of Attorney).  Neither of these allow the agent under the power of attorney to admit someone to a facility.  If someone lacks legal capacity to provide for their own food, shelter and medical care or to manage their own finances, a court can award a guardianship.  While a guardian of the person can decide where the person lives, this does not extend to involuntary commitment.