Does she have a right to sell the home and keep the money from the sale?

It is difficult to precisely answer your question without looking at the POA and what it actually states, but in general, your sister would likely have the power to sell the house, regardless of what your mother's will states. The money from that sale would be your mother's and would not belong to your sister.

As I understand your question, your mother can no longer live alone. Your mother owns a home in Arizona and your sister who has power of attorney for your mother has indicated that the home is to be sold. Your sister may be taking this action because the funds to be derived from the sale of the home are needed to cover the cost of care for your mother. You have not indicated if your mother is competent at this point to make decisions. Not being able to live alone could be attributable to health issues not mental incapacity. In any event, your sister, who is authorized to act as your mother's agent through a power of attorney document, should not take such action if your mother is competent, unless directed or authorized by your mother. If your mother is incapacitated, and the power of attorney is what is called a durable power of attorney, your sister may act to do this for your mother's benefit. Your sister may control the funds received for your mother's benefit but the funds do not belong to your sister or her family. If there are funds remaining at the death of your mother, if your mother's will provides that her assets are to be split between her children, your sister will be entitled to a share just like the other children are.

As the Power of Attorney, she has the rights enumerated in the POA document, which may or may not include the right to sell the home; however, she would not have the right to keep the proceeds for herself. The POA lets one act on behalf of another - not take one's property.

In Oregon, she would have the right to sell the home to take care of your mother's needs. However, the sale proceeds would have to be deposited in your mother's account not your sister's.

Selling a home in Arizona is a matter of Arizona law. Under Oregon law, with a proper power of attorney yes, your sister can sell the home, and no, she can't keep the money. The proceeds of sale of your mother's home are your mother's money. Power of attorney does not give the agent the right to take the principal's money. If your mother cannot live alone any more, and needs to go into a care facility, the money from the sale should be applied to pay for her care. I suspect this would play out the same under Arizona law, but as I said, if your mother is in Arizona then Arizona law applies and you should consult an Arizona attorney.

It depends on the language of the power of attorney. You have no "right to inherit."