Me personally I would just talk to your daughter about the behavior she sees in this girl. Talk to her about how it makes her feel and how she should never do that to someone else. Help her deal with the disappointment of not being included and trying to not let it bother her so much.
I would not talk to the girl's mother. That makes you look over-protective and whiney. It makes your daughter look pitaful. Just let it go. Your daughter doesn't need mommy jumping in to such a minor situation. Now if the girl was threatening your daughter with physical harm, then I would address it with the mother....or police in some instances. If the girl was doing something equally dangerous, then yes. But you can't protect your little one from mean peers.
I can sympathize with you. My daughter is generally very sweet and kind to everyone. She has even been rewarded at school with prizes from the vice principal because she was caught being kind to a little boy that was being teased. So I know she's got a big heart. (though she does try to be mean to her little sister)...anyway, she has an older cousin that she just adores. On several occasions throughout the past six years I've seen her older cousin do and say really mean things to my daughter. My first instinct was to go in and set her cousin straight....or even tell her mother what a hateful little girl her daughter was being at the moment. But I held back. I talked to my husband because it's his family and we decided that our daughter has to learn to handle these kinds of situations. We talked to her about how she felt when her cousin was mean to her and we talked about how the behavior was really bad. We told her that her cousin loves her and sometimes people we love do things to us without thinking. We told her that next time she should look her cousin in the eye and ask her why she's being mean. Then tell her "I love you and I don't want you to be mean to me."
In several situation now we have told her to look the person right in the eye and ask them why they are being mean and if it feels good to hurt her. She will tell them just that and explain that she wants to be friends. If she gets a bad response then she knows she's supposed to say to them well I'm not going to play with you as long as you are being mean. (She's never to say I don't want to be your friend or use that line just because someone isn't doing what she wants....because she's tried)
Anyway, she is getting very good about confronting others when they are ugly to her or even other peers. She isn't ugly or mean/confrontational....she's been taught to be kind, but direct. We have taught her what to say depending on the response. But she's always to be kind and polite.
It has worked with her cousin and they play great together. It has worked with two boys that were picking on her on the bus....one apologized for being mean and the other just left her alone after that.
So sorry about the novel. I thought I should clarify what I was telling you with my own experience with my 6 year old.
PS I forgot to mention that the reason I THINK you shouldn't talk to the mother is because my mother tried to help me once with a little boy that was teasing me. In the end she made it way worse for me and then the whole bus joined the fun. That had to be the worst year of my life. At that age I'm not sure it would turn around on your daughter, but it could.