When you are named as a financial agent under a general power of attorney, you have the right to undertake any action the principal could undertake herself. This includes applying for bank loans on her behalf or refinancing the loans she already holds.
A power of attorney, or POA, is a legal document used by an individual to appoint an agent to act on his behalf in either financial or medical matters. The principal can limit the agent's authority in the document, but general financial powers of attorney confer broad powers to do anything the principal can legally do himself. A POA agent is under a legal obligation to act in the best interests of the principal.
Unless the terms of the financial POA document limit your authority, you can refinance your principal's mortgage if you determine that it is in her best interest to do so. You will have to establish to the satisfaction of the lending institution that you hold legal authority to act on the borrower's behalf.