This is so tough. I feel your pain. My 12 yr old daughter has had some trouble navigating social waters over the years. She is very friendly, and would be everyone's friend if she could, but most girls are not this way.
Her most recent struggle has been with a friend who started to pull away at the beginning of this year. It was difficult and confusing for my dd because at the same time as she was pulling away, she was playing mind games and making my daughter think she really still wanted to be her friend. I had to have many, many conversations with her pointing out the reasons why this girl isn't a true friend.
In your case, maybe the friend isn't playing these games and has really just pulled away. I think it's OK to tell your daughter something like "Look, at this age, it's normal for girls to want to change friends. It sounds like that is what "Katie" is doing. Does it hurt? Sure, but there isn't much you can do about it. You can't force someone to be your friend. You have to let her go".
These talks seem to help my daughter. And when she was confused when her ex-friend would sit by her at lunch one day, or want to work on a project with her, I'd tell her that she shouldn't get her hopes up. It's more likely than not that this girl wants something from her, or is afraid of getting in trouble. She saw me talking to her mom at a recent basketball game, and I noticed she was acting very chummy towards my daughter for a few days after that.
As for the other mothers getting involved, I would reiterate that you are talking to your daughter and trying to help her move on. There is not much you can do outside of that. You can't be at school with her.
Were these girls always a threesome, or could you set up some play dates or outings with just your daughter and the other friend who hasn't pulled away? Is your daughter involved in sports or programs outside of school? If so, maybe you can try to foster some friendships with girls outside of school.
And lastly, I would suggest you get some books for her on navigating social situations. American Girl has a few, and I think they have really helped my daughter.
Best wishes! I know how hard it can be on mom when our kids are having a hard time.