I am from NJ. I wouldn't call it a filing since it doesn't have to be filed with the County. Its Mom assigning POA to you. She can have no Dementia. She needs to go to a lawyer, tell him her wishes and who she is assigning. She signs in front of a Witness. To me this is a clean POA. I was POA because I was the child living closest. But my brothers were aware.
Basically the POA is between the one who appoints someone, your mum, and the one she chooses to appoint. No one should exert undue influence to get anyone to sign a POA. The person appointing the POA must be competent. As others have said, no one else need be notified