A power of attorney won't allow you to send your mother away against her will. You need a seek guardianship or begin an involuntary commitment proceeding. If her condition is bad enough, you can report her to Adult Protective Services for self abuse and self neglect. Contact an elder law attorney to discuss your options. Good luck.
You could apply for guardianship, but that is usually a somewhat slow process, although there are "emergent" procedures in many jurisdictions. Involuntary commitment may be possible. I would contact the local social services agency (i.e., Board of Social Services/Welfare)
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature. Visit Steve Zelinger's website: http://www.stevenzelinger.com/
Because taking such an action would deprive your mother of fundamental rights, there are a number of legal protections built into the process of having someone committed against their will. I recommend that you consult with an elder law attorney (www.vaela.org, click on "find an attorney" and enter your zip code) about what your options may be to assist/protect your mother.