Am I correct that even though a mother gives her daughter a power of attorney we could still conduct business with the mother "if" we choose?

A power of attorney does nothing to change the rights of the grantor to act on his/her own behalf. The POA is the creation of an agency relationship that allows the attorney in fact (AIF) to act on behalf of the principal, but does not in any way prevent the principal from acting him or herself.

Only if an individual is found incompetent by a court (or has not reached majority) is the individual prevented from acting on his/her own behalf. Then the party acting on behalf of the individual becomes a conservator or guardian.

Thank you very much.