You are right; the Social Security Administration does not honor durable powers of attorney. Powers of attorney are created under state law and are not necessarily binding on federal agencies. A representative payee manages benefit payments for beneficiaries who are incapable of managing their Social Security payments. You need to contact your local Social Security office to apply to be a payee.
If you do become representative payee for your mother, her Social Security payments should not go into your account. You should open a separate account to receive her benefits that should be in her Social Security number, not yours. You may be able to continue to use her current account, but you will need to discuss this with the bank.
For more information about representative payees, click here.