Hello, Heidi. I am a customer service consultant in the Boston area.
The issues you are experiencing are not unusual in the world of service personnel. There are always some tough employees who insist on doing things their way, and who let their moods dictate their interactions with customers and fellow-workers. It always boggles my mind as to why these kinds of people sought service-related positions in the first place, and how they were actually hired to be in these positions. I have always maintained that the primary criteria for any customer contact position is a desire to be of assistance to others. Industry and product knowledge can always be learned, but the heart-felt ability to help others is something that defines a person.
That said, it seems like this is the time you need to have a sit-down with your troubled emplyee, and let her know that the requirements of her position include being courteous and helpful to all customers, and being able to take direction and instruction from her manager. These are non-negotiable points, and if she is not adhering to these requirements, she is not adequately performing her job, and is therefore not of any use to the organization.
Sounds harsh, but these are critical issues here. Customers are won, and kept, with every interaction. All it takes is one bad experience, and a customer will walk away, and take a lifetime of business with them (not to mention all of the potential business from others whom they will tell about the bad experience). If this happens once, it is bad. If it happens several times, your organization will feel the pain. As a customer service manager, you can not allow it to happen.
As for dealing with the "lifers," this is another situation that many of us have had to grapple with. You were obviously put in the manager's position for a reason. I don't know if you were formerly a peer of the lifers or if you came in from another department or organization. But either way, the situation is the same. You have been given goals and standards by senior management, and your job is to get your team to achieve these. One of the toughest things for me to grasp when I first became a manager (way back when dinosauers roamed the earth!), was that I did NOT need to have all the answers, all the time, to justify my title. The best advice I ever recieved was to encourage participation from my team. Obviously, the final call was mine as manager, but getting ideas and comments from the people who were going to have to work under my direction was crucial to their buy-in. This is where the lifers may have some really valuable input for you. Don't be afraid to tap into those resources, and to give them public credit for their input. If done correctly, these are the kind of employees who can allow you to shine as a manager.
However, with both your troublesome employee and your lifers, the bottom line is that you all have responsibility to the organization's goals, and the best way to achieve those goals is to lay them out on the table, and roll up your sleeves, and say, "Folks, this is what we have been directed to do. We are in this together, so who has some ideas as to how to make this work." You can do this! This really does work, if you are sincere.
If I can be of any assistance in your endeavors, please feel free to contact me.