Charles Helliwell's Answer:
You will find that this is commonplace behaviour in many organisations, so don't be too dis-heartened.
Your colleague is one of many who relish the prospect of authority without responsibility. It is behaviour most often displayed by those who have been passed over for promotion for whatever reason, and stems from the resentment and frustration they feel.
On the other hand, often these people have a history of service with their respective organisations and possess significant knowledge to back it up. That makes them both vulnerable and insecure and consequently dangerous to a new manager.
Your colleague will seek to disrupt your tenure as a way of demonstrating her value and capability to your organisation. The question you must ask yourself is are you better off compromising and complying with this individual in order to harness her knowledge and capability or disposing with it altogether and starting again ?
Both options provide an element of risk, which you must assess in terms of your own well-being and the future well-being of your group and the organisation.
My own recommendation would be for you to 'OUT' this particular individual. In other words impose the responsibility she chooses to shun with the authority she craves. One way to do this will be to make her the 'gatekeeper' for mistakes and errors.
In other words, make her responsible for troubleshooting solutions in your department. Her responsibility will be to report these, in tandem with her recommendations, to you on a weekly basis.
She'll either have to put up; or shut up, and frankly, you won't really care which.