There are some employees who are backstabbers, but you have one who is a "front-stabber." She apparently has no qualms about making potentially damaging comments about you right before your eyes.
Although you are showing a high degree of corporate gentility by refraining to say anything to her about this behavior, you may be doing yourself a disservice. If your manager appears to be buying what she is saying, you should rethink your reluctance. This does not mean that you should jump all over your employee when she takes a shot at you, but you should take action when she plays this card. You should be clear and concise and simply correct her comments in a businesslike way. This will send a message to her, as well as a message to your manager.
In addition, this is a matter you should discuss with her in private. Give her some specific examples of her cheap shots in front of your manager, and let her know that you regard this as unacceptable behavior and you expect it to stop immediately.
Unless your employee stops playing this power game, she is going to power herself right out of the company.
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