You will find that this is a commonplace behavior in many organizations, so don't be too disheartened. Your colleague is one of many who relish the prospect of authority without the responsibility. It is behavior most often displayed by those who have been passed over for a promotion for whatever reason, and stems from the resentment and frustration they feel.

On the other hand, often those people have a history of service with their respective organizations and possesses 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 to demonstrate her value and capability to your organization. The question you must ask yourself is are you better off compromising and complying with this individual to harness her knowledge 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 organization.
My own recommendation would be for you to 'OUT' this particular individual.
In other words, impose the responsibility she chooses to shun with the responsibility she cares. One way to do this will be make her the 'Gatekeeper' for mistakes and errors.
In other words, make her responsible for troubleshooting solutions in your department. Her responsibility would be to report these, in tandem with her recommendations, to you on a weekly basis.
She will have to be either put up, or shut up; frankly, you won't really care which.