Managing an arrogant producer

I'd like to get some perspective from other Managers on the following situation.

I just listened to the podcast "Mananging an arrogant producer", and I took away some great strategies and action items. I would like to get a more specific ideas on how to handle this particular situation.

I had a previous job in a management position with another company about 2 years ago where I was terminated due in part by my performance.  I say due in part by my performance, because I didn't give an assistant manager any negative feedback on her lack of support with myself. This assistant manager thought she was running the show.  She met with my boss frequently and undermined me with the team and my boss. 

My problem now is that it is happening again.  I have a direct report that was hired the same time as me. I was promoted. She wasn't. She is a top producer. I've had O3's with her.  I've also had conversations on how we can improve our working relationship.  I believe she is spreading rumors with in the team that we don't like each other or that I am a bad boss. I don't have proof of this other than hearsay. 

She thinks that because she is engaged with the business she is running that I need to be just as engaged in her business (knowing the detail) that she is.  I told her I would I would get better in the smaller stuff.

What I'd like to know at this point is how do I manage her, going forward.

She is disrupting the team as well as undermining my ability and credibility  that I have established with my boss as well as the team.