You should get dad to an attorney.
Your mother, if she is not competent, can not execute a power of attorney. If someone needs to act for her, a different court action (guardianship) is going to be necessary. Your father however may wish to provide a power of attorney for himself. Also, POAs die with the person who grants them, so you will need other things in place to deal with her affairs in the case that she (or dad) passes.
While he's at the attorney, he'd be well advised to get durable and medical POAs for himself as well as advanced medical directives. It's also a good time to look at estate planniong (wills, trusts) if they have not yet done that.
Yes, the guardianship and the POA can be crafted that one of the children can take over if the father dies or is incapaciated.

