If I'm the executor of my aunt's very small estate but her attorney has mishandled things. can I pay her, fire her and then let my own attorney finish the paperwork?

You can always fire an attorney.  Ethical rules for attorneys in all states allow clients to fire their attorneys for any reason, or no reason at all.  You are correct that you are almost always responsible for fees earned up to the time you fire the attorney.  Check the contract with the attorney to find out what fees you might owe.