You and your sister can each report half of the interest on your individual return - or you can report it all on yours. Enter the 1099-INT as if you received it from your mother. The payor should be the estate but it might be your mom. Then you need to get things fixed so it makes sense that you claimed the income.
I am guessing you are not filing an estate return or the money would be going on the estate return. Instead, you should receive the income as nominee from your mother. Normally, she would file a 1099-INT to each of you from her, see General Instructions for Certain Information Returns. You can file the forms for her.
Next, you need to actually do the things that must be done when someone passes. All bank accounts should have her name removed, notify credit bureaus, cancel driver's license and voting, and so on. Leaving her name on a bank account opens her up to identity theft and can create many more issues for you. You need to shut down all venues for people to wrongfully steal the house and money from you. Be sure her name is not on the house title. I am very sorry for your loss.
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