I think going to the administration is over the top and misses a chance for the OP's daughter to learn how to handle a tough situation herself. My advice is the same as it would be if this were a group of adults and an acquaintance was trying to insert herself into a group event to which she was not invited. "AG, I think maybe there was a misunderstanding. We have a group that already made plans and we won't be adding anymore to the headcount." And then at the dance if AG won't leave her alone. "AG, I'm going to excuse myself. " (walk away without waiting for a response) And if she STILL won't leave her along. "Hey there AG, I know you don't mean to, but you're monopolizing all of my time. I'm going to excuse myself to go chat with some friends. Can you please give me a little space for awhile?" It's unpleasant but it's the only way. That and asking her friends to rescue her, "Oh, hey, AG. Sorry for the interruption. I need to grab OP's Daughter. Please excuse us."
I think this summarizes my thoughts best. If AG seems to think she's included in official pre/post-prom plans, that needs to be corrected right away, before she tries to tag along to a private event. While at the actual prom, I don't think DD can expect to never interact with AG, as it's a "public" venue, but she can say things like, "Well, it was nice talking to you. I'm going over here now. Hope you have fun," followed by, "Actually I wanted to talk to Mary and Bob by myself. I'll see you around," followed by, "AG, I feel like you've been following me around a lot tonight. Could you please leave me alone for a while?"
And I think she should talk to the friends in her group about this, and make sure they're aware that they shouldn't invite AG to any of the festivities on their own. I mean, if they truly want
to, that's a different issue; but assuming they don't, they should strategize about how not to get guilted or otherwise manipulated into inviting her. Like, everyone in the group knows that AG isn't invited, so if AG claims one of the others said it was okay, they will all know she's wrong. Probably more than one of the girls in DD's group feels sorry for AG; but if any of them cave, all of them, especially DD, will suffer for it. And maybe they would all find it both educational and somewhat entertaining to roleplay amongst themselves about politely deflecting people.
I was in sort of the "middle tier" in high school--not popular, but not a misfit either. Sometimes people hung around me and my friends, and seemed to feel like we were better friends than we actually were, simply because we weren't mean to them. Mostly it was okay with me because I personally didn't do much social stuff, so they didn't have an opportunity to cling to me. But I would always see them hanging around the edge of our group, or sitting at the end of the lunch table awkwardly. I don't recall people actually ignoring them if they spoke, but people definitely didn't try to draw them into the conversation, either; and often this made the point that they weren't actually friends with us. It would have been really uncomfortable if they had been more "outgoing" like AG is, and actively tried to insert themselves into things.