A person who finalizes a power of attorney naming another person to act as his or her agent must know and understand the meaning and effect of the document. While
mild Alzheimer's doesn't usually prevent this, trickery does. So if your sister truly used that sneaky tactic to get your mother to sign the power of attorney, the document is not technically legal"”and your mother is free to revoke it, or you or others could challenge it in court.
I don't in any way condone the trickery, but from a practical standpoint, that might not be what you want to happen. That's because your question raises a number of other questions"”and the answers might help you all find the way out of the thicket you're in now.
First, is your sister actually empowered to act as your mother's agent now? Some powers of attorney are written to take effect immediately, but very few of them. Most specify that the agent is empowered to act only when a person becomes mentally incapable of making his or her own decisions"”and that condition must be verified in writing by a doctor, sometimes two of them.
So the first step may be to take a hard look at the document that's causing this distress. If it's like most POAs, then it specifies just what you would all want to happen: your sister would take on duties as agent only if and when your mother is not able to act for herself. Most people who have POAs in place do it as a matter of good planning while they still have the good reasoning and capacity to do so"”and your mother needs to understand that.
If it's a usual POA that empowers your sister to act only if your mother becomes incapacitated, than she has no power to act now"”and she needs to understand that.
While two siblings are sometimes appointed to act jointly as agents under a POA, it is usually a bad idea, and wiser to name just one person for the job"”and you need to understand that. It sounds as if you may well have your hands full being the more sensitive, attuned one, anyway"”so there will be plenty other ways for you to help, now and in the future.
Second, do you want to start over"”or just get a clear understanding on the table?
If your mother's alleged power of attorney document is one that takes place immediately, it sounds as if it's not what your mother wants. And if it's one that's slated to take effect only when absolutely needed, then in an ideal world, you could all agree about what it means and when it will"”and importantly, will not"”take effect.
A good and honest talk with all three of you at the table might help clear up the hurt and misunderstanding here. If that sounds too much like forcing a round of "Kumbaya ”in a bad way"”then you might call in another person to help with the conversation: a lawyer, a family mediator, even a trusted and knowledgeable family friend.
Another option, given the bad blood already spilled over the current document would be to start all over"”this time with full disclosure. Again, bringing in an objective third person might be a lifeline for all you family members who are feeling a bit lost at sea.