You said your daughter cries because she feels bad about being horrid to people. I have to say, I wish more people felt guilt for being mean. She and you ought to be proud of her for having developed a sense of responsiblity for her words.
If the other mother is a friend she should want to help the girls come to an understanding, not add fuel to the fire. Seems to me, that if mom is setting an example like this, then the daughter is probably not going to be inclined to behave differently.
Wish I had better advice.
Good luck.