I believe the core issue is whether your daughter feels she needs you to advocate for her in this particular situation. If she looks to you to help her with a situation she feels she cannot handle alone and you turn her down because you are uncomfortable talking with a fellow teacher, then a message is sent; the message is that your being a teacher in her school makes you feel uncomfortable about talking with any of her teachers whom she has a problem with. I am most concerned by the larger issue that this particular situation raises.
Let's face it, there are always going to be issues like this that surface for you and your daughter. You and she need to come to an understanding about what she and you can expect from each other when these situations arise. Good luck. I'm sure you'll reach a satisfactory decision.