N.L.
DEFINITELY an important issue to continue adressing. I feel bad for you that it is coming on so strong so early... but at the same time, it's a golden opportunity to help your daughter build these skills now. Very good job so far though- honestly.
OK- 1st suggestion, read! Educate yourself further on the subject. First book that comes to mind is "Odd Girl Out," it will really deepen your understanding of what goes on, how, etc. etc. which will really guide how you intervene.
2nd suggestion- Role play. Really help your daughter feel safe and secure enough to tell you exactly what this girl says, how she goes about it, etc. Then ask her how she might respond next time. Sit there for a while. Then gicve her some answers as to how. She'll have the anxiety of what might then happen, how the girl might react, and that is what you want to role play handling. Also, it will help if you teach her to use the language they used in that training they did. And, it will certainly help if the school does a follow up and plans to do interval follow ups to the subject.
Hard as it may be, try to remember that the "mean" girl is just a girl also. She's lost HER way with interpersonal skills and needs help too. If you do go the route with talking to her mom, make it as natural and informal as possible. Draw her mom out to talk about what it's like for her in trying to help her daughter with this. You'll be much more effective then to march in with a list of complaints and examples. You CAN relate to the other mom's position, you're just on different ends of the spectrum but can certainly be unified in dealing with both your daughter's issues.
And as I think you are already perceiving, it IS an issue for your daughter to learn the skills neccesary to maneuver this situation. Even if magically this mean girl disappeared or began being nice, this is for certain a pattern and a type of person that will repeat itself in your daughter's life.
Good luck!