There is no regulation requiring an LTCF to have ADONs. Hence duties and responsibilities are "set" by individual facilities, authored of course, by the DON. If your facility's organizational chart depicts you as second in command to the DON, then you assume all responsibilities designated to that DON during his/her absence.
In your case, you guys get to do all the tasks, the DON simply oversees the process (and still gets the glory

).
Discreetly ask for the DON's job description. Hey, you'll never know you might be stepping on her toes

... or, doing a job she's supposed to do
To succeed with your new role, (quote) "Don't waste time telling people what you are doing or what you are going to do. Results have a way of informing the world."
Good luck!
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