That sounds like a difficult situation. Without seeing the durable power of attorney, we can’t give you a definite answer. Some powers of attorney are effective as soon as they are signed and others only become effective if the person granting it becomes incapacitated. The latter are called "springing" powers of attorney. If your mother's document is springing, then your brother cannot act until her incapacity is determined, usually by a physician.
But assuming the power of attorney is current, your brother can go to the bank to gain access to your mother's account and pay her bills. That is his legal power and it may go smoothly. On the other hand, the bank may feel it needs to notify your mother, or she may discover what your brother is doing on her own. In either case, she may revoke the power of attorney. If she objects to the payments, the bank may view that as a revocation. Either way, nothing ventured, nothing gained. So, assuming the power of attorney is not springing, we would recommend that your brother go to the bank to seek access to your mother’s account to pay her bills.
For more information about powers of attorney go here: http://www.elderlawanswers.com/powers-of-attorney-come-in-different-flavors-8217.