Only the title holder (owner) to a bank account has the authority to use the ATM card. If the decedent (mom) was the sole owner of the bank account, then the answer is "no", you cannot legally use that ATM card and should not; even if you are a signer on the account, then your right to withdraw funds from the bank account terminates upon your mother's death. If the account is titled in the name of a "living trust", AND you are a current trustee, for which the bank has records to substantiate your fiduciary authority, then you likely could withdraw money.
I do not know what you mean by "I have access to her accounts"; so, under the extraordinary assumption that you may be a joint tenant on the account with your mother, then you may also have a right to withdraw money from the account after you show the bank a death certificate.
Nevertheless, because you discuss in your question probate, a will, and "less than $50,000"; the best thing you can do is make an appointment with an Arizona estates and trust attorney to review the potential issues in your case. Don't wait.
DISCLAIMER: This answer does not create an attorney-client relationship nor will the answer provided be considered confidential. The attorney providing the answer has not been retained to represent the indidivual who has asked this question. This answer is not legal advice and must not be relied upon in making any legal decision or legal action. It is necessary to seek out the advice of an attorney before you take any legal action.
You cannot access a decedent's accounts after her death. If you are named executor and the will has not been probated, you can pay any expenses yourself (with your own money), and seek reimbursement after the estate is admitted to probate.