Once you have all the facts, it's time for a conference at school. If your daughter has other teachers, you might invite them to explain how she behaves in their classes. This way you'll have a more complete picture of your child's behavior at school. In situations like this, the more heads the better.
The purpose of the conference will be to define how your daughter should behave in the classroom and to decide on the consequences that misbehaving will set in motion both at school and at home. You will also have to decide how any further misbehaviors will be communicated to you. Email sounds like a good idea.
At the end of the conference, the behavior plan should be presented to your daughter in front of the group by one of the participants. She needs to know exactly how she is expected to behave in the classroom and what will happen if she misbehaves.
You cannot excuse your daughter's behavior. You must make it perfectly clear to her that it is unacceptable for her to be rude to her teacher and that there will be consequences every time that she is. If she misbehaves at school, you could have her stay in her room after school or watch no TV that day. Be patient and expect some backsliding as your daughter learns to behave appropriately.