Dan Bobinski's Answer:
I feel for you, David. Your top sales person is certainly valuable and you are wise to want to keep her. But considering how much you lose by replacing people who quit because of the environment she creates, you are even more wise to find a way to make her more of a team player.
In other words, since the average cost to replace an employee in the US is $38,000, you are wise to invest heavily in some one-on-one coaching for this individual, as it will actually save you money in the long haul. It will also bring you even better returns after her co-workers feel the difference and become more productive.
Because I have no information on what you've done to this point to address the issue, let me suggest a three-prong approach.
1. You've done a good job of identifying specific behaviors that are "unacceptable." (Screaming at colleagues, specific instances of gossip, and talking rude to customers.) These need to be brought to her attention through an official HR meeting and documented in her file. But to bring her onboard with the idea to change (and also to avoid alienating her), a big-picture needs to be painted in which she can see how her role is important to the company-but also how the ripple-effects of some of her actions are detrimental to it.
In other words, show her that you're not only committed to her success, but also to the success of the company. I'd recommend using questioning techniques to draw out her thoughts and insights about how her actions affect the company's operations. This will help her "own" the issues and minimize the feeling that she's being lectured. The idea is to partner with her, not scold her.
2. Open a dialog on how you intend to help her overcome some of the detrimental behaviors through coaching and accountability. Emphasize that the company is going to pay for it. The coach should be someone outside the company. Offer her a choice of coaches or let her choose one for herself. I'd recommend the company pay for high-quality coaching with an experienced, proven coach (remember, if her actions cause someone to quit, it's going to cost you $38,000 anyway).
An example: A few years back a company called me with a similar situation. We did a 360 on the person and his scores were horrific. The person was told changes had to be made or he would be let go. After five months of coaching we did another 360 and the scores were remarkably better. People actually enjoyed working with him and productivity was much better all the way around.
The key will be to identify specific behaviors and attitudes you want to see, and make sure you, her, and her coach are all in agreement on what these are.
3. Come to agreement with her on when to hold short follow-up meetings to measure progress on specific milestones. These should be fairly frequent to keep them top-of-mind. Meeting every three or four weeks is good. If you go much longer than that you won't see much change as the issues will fall to the back burner.
Ensure those meetings happen, and keep an attitude of partnering, not monitoring. Miss those meetings or gloss over them and she'll quickly assume you don't really care-and then neither will she.
Bottom line, if she can see the bigger picture and how the ripple-effects of her actions affect the company's bottom line, she is more likely to agree that changes are in order for her own long-term success.