@cj8892 All good advice! I have also been through issues like these as a caregiver several times and there is sound reasoning behind all of the recommendations.
As @EveRH noted, it is important to document your mother's diagnosis of "dementia" and then to get your "ducks in a row" as far as legally assuming responsibility for all her affairs. If she has dementia, then the matter is not quite as simple as making the necessary decisions and signing the papers. If she cannot understand what she's signing, then it is of no legal value. If you have POA for medical decisions, that is not the same as having a general POA. The "elder" attorney can guide you through this process so that you will be able to move ahead to act in the best interests of your mother.
It's also important to remember that a POA ends with the demise of the individual requiring care. If you are also to be the executor of her estate, the attorney will then help you through the qualifying and verification process at the courthouse in order to proceed with closing out her estate. Each state may differ in it's requirements.
@GailL1's suggestion to remove your mother from your bank account should be done as soon as possible for the protection of your own financial interests. In order to be scrupulous in your record-keeping for your mother, especially if there is any size to her estate and you have siblings where there is the possibility that heirs may have differing opinions, you should make the necessary changes to HER account and leave a copy of the paperwork for the POA with the bank.
I also agree with @nyadrn's comments. Your mother may have experienced an issue or incident that caused her discomfort in some way...mental, physical or even a psychological shock...and she is unable to communicate it in the usual manner...ergo, the decision to "move" from her present quarters without any clues or explanations about the "why!"
Individuals with dementia cannot be relied upon to make sound decisions minute-to-minute nor day-to-day...about their personal business not their personal care and well-being, so leaving her alone for any period of time is taking a huge risk...and as @GailL1 reminds us, it is the disease doing the damage...she has no control when it comes to making sound decisions if dementia has subsumed her formerly competent mental function.
All peace and good wishes to you and your family...
"Never succumb to the temptation of bitterness." ~ Rev. Martin Luther King, Jr.