How do I designate a back-up POA?

You're wise, and honest, to address this situation now. Let us know after you've read the POA document and if necessary posters can suggest alternate options.

Thanks. She is not of sound mind, so I am not sure I can do this. That's my concern......

First read the POA to see if it authorizes you to do this (mine does). If not, you'll have to have your mother create a new one which provides authority for you to designate an alternative, or successor, or your mother can do this in a new POA which she creates.