Wow, I feel very sad for this girl. But I also completely understand how annoying her behavour must be for your DD and her friends.
I think there's two issues here:
1) AG trying to insert herself into the pre-prom and post-prom plans; and
2) The possibility of AG clinging to your DD at the prom all night long.
Issue 1 is easier to resolve. As others have said, your DD needs to let her know BEFORE prom-day that she isn't part of that group's plans. I believe it is possible to do this kindly but firmly. Eg "Hey AG, the other day you mentioned something about us going to the prom together. I should have told you at the time, but I've already made arrangements. I'm going with my group of friends. But I'm sure we'll see each other at the actual prom."
If she says "Can I be part of your group? I'm just one more person, etc", your DD should reply with "Plans have already been settled. It's not going to be possible to change them."
(It will also help if the pre-prom celebrations aren't taking place at your house. If another girl is hosting, that lets your DD off the hook somewhat.)
Issue 2 is tougher, since - as PPs have stated - people are expected to mingle somewhat at the prom. As such, I don't think your DD (and her group) can really demand that AG keep her distance all night. I remember at my school ball, most of our time was spent in a loose circle on the dance floor, bopping to the music. There actually wasn't "that" much conversation happening. If your DD's dance is the same, I think it would be a kindness to let AG join their "dance circle".
That said, if AG latches onto your DD and follows her around all night, that's a different story. Your DD shouldn't have to put up with that. I've found that a good approach is to say "Hey, why don't we go and talk to Ted and Alice?" Then after a few moments conversation, DD can move onto a different group, leaving AG to chat with Ted and Alice.
Of course, there's the chance that AG will leave Ted and Alice, and run after DD. In which case, I think DD can be more blunt, and say "Hey AG, you don't have to follow me around all night."