If the Principal Lacks the Capacity to Grant a Power of Attorney
In the event that a determination is made that the principal lacks the requisite capacity to sign the Power of Attorney, in order for someone to have the power to act on their behalf, a Guardianship proceeding would have to be commenced in the New York Supreme Court. While this is an alternative which must sometimes be relied upon, the preferable course of action is to have your mother execute a Power of Attorney when she can still make decisions as to who should act on her behalf.
If you are uncertain about the capacity of a loved one to sign a Power of Attorney, it is best to consult with an attorney experienced in estate administration and guardianship proceedings.