The individual, or individuals who are authorized to act for your mother's estate should handle the finances. And any instructions that govern the estate (like a will or trust) should also be consulted before any expenditures are made to make sure that what occurs is consistent with her wishes. If you're the one that's authorized to act for the estate and paying bills isn't inconsistent with any applicable documents or statutes then you can proceed. If you're not sure, it might make sense to consult an estate/probate attorney to make sure before you do anything further.
Evan A. Nielsen is licensed to practice law in California and handles federal tax matters throughout the U.S. The information provided here is for educational purposes only and is not intended as legal advice for a particular matter. This response does not create any attorney-client relationship with the author. For specific advice about your particular situation, please consult an attorney.
The income belongs to the Estate. Is there an Executor?
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You should consult with an attorney. Whoever has the authority to act on behalf of your mother's estate is qualified to disperse the funds earned by the estate.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained