POA needs to be reviewed. If no guardianship or conservatorship has been established and she is able to make her own decisions, I don't think her mother can make her move. I have POA of my elderly father, but it is to be able to sign and make decisions, if he is unable to do so. I added two tags to your question, since a probate attorney in NM would be able to provide the best answer since you are a NM resident.
No. The disabled person is still in charge, and if necessary, can revokes the power of attorney at any time