I agree that it can't be done *effectively* without hurting this girl's feelings, but it still can be done nicely.
And the OP's DD and her friends need to realize that they do NOT have to worry about not hurting her feelings at all.
They only need to worry about not GRATUITOUSLY hurting her feelings.
So the DD can say, "I'm sorry--I have plans to spend the night with a group of my friends. I can't include you."
She should say it right away. And pleasantly. Without *too* much regret.
Your DD needs to internalize the idea that she is not being rude--that this girl is in error. Sort of like, her zipper's undone or something. That this girl has wrong information and your DD is actually honor-bound to *correct* it. And that's what she's doing--correcting her, not rejecting her.
It will help if she also internalized the idea that the "party" is not hers alone, and so she is not authorized to include this girl in the party. (even if she is the one who would most object to her being included)
And your DD may need to gear herself up for saying, "I'm sorry, but I
don't want to can't spend prom with you. I have plans already." (the second time she has to say this, she should add on, "with my friends" (implication being, you're not one of them)
(In fact, your DD *does* have "a date"--all the rest of her friends are "her dates," and so that's what she needs to say. "I have plans.")
Then, to make herself feel stronger (and better about herself), she should remember: Once she does say, "I have plans with my friends, adn I can't include you," this girl should get a clue. If she doesn't, then your DD is now in self-defense mode, and she is entitled to feel a little bit resentful.
(also, the sooner she does it, the better. It's kinder to the girl, for one. And easier on her because she'll have it over with and will have time to fix it so
Meanwhile, you and DD might role play some ways to completely discourage conversations with this girl at all--how to arrange so that your DD's lack of interest in a friendship is clearer.
Toots has given you good starter words.
I do think it would be better if this were discussed privately before the prom so the girl isn't sitting there all night waiting for your daughter to show up and then glom onto her the second she walks through the door like she did at Homecoming.
I wanted to add my two cents about this. I think some things need to be said and some don't - this is what will affect how much AG gets hurt. IMHO DD does not need to say anything to suggest that she does not like AG and does not want to hang out with her - that is unnecessarily mean. If you don't want to be with someone, don't say so and make a point of telling them you don't like them! So don't say "I don't want" - say "Sorry, I can't." DD should use her etiquette obligations as a shield - she can't hang with AG because she already promised the night to her other friends.
I would recommend "Sorry with a Smile" - since AG is so oblivious and prone to steamrolling, all responses to her should be bright and informative as if DD is doing her a favor by kindly correcting her assumptions:
AG: Oh you and I are going to have so much fun with *AGs other friends* at Prom!
DD: *big friendly smile* Oh I know we'll all have fun...*serious frown* But sorry AG I can't hang with you, I already made plans to go to Prom with *DDs own group*. I didn't get a chance to tell you before, you should have asked me sooner - oh well! *Brilliant smile again* I'm sure we'll all have a blast right? Woo hoo Prom! Are you *BEAN DIP OUT TO WAZOO!* blah blah prom dress yadda yadda oh look at that I'm late for class bye!
Now, if AG insists that they can ALL hang out on Prom, or moves in to cling when DD gets there, DD can act surprised and amused and put AGs behavior off as silly for both of them. Instead of saying "Get away from me," she should redirect AGs attention to *food/music/hot guy/wow what is she wearing etc.*
AG: I'm going to hang with you!
DD: *lightly* Oh why would you want to hang with me, you have So and So and she's so cool are you guys *bean dip*, well I'm off to *whatever*. I'm sure we'll see each other around,
AG: I'll come with you.
DD: Oh you are so sweet but that would be mean to *AGs posse* you don't want them thinking you ditched them for me.
AG: Then we'll all hang together.
DD: Oh that would be fun but we came to hang as *DD group* and *AG group* we'll just keep it that way.
AG: But we could all-
DD: Yeah I know it would be great but I'm just hanging with *My group* tonight. Have fun with *Your group*!
AG: Oh come on... *makes a move to latch on*
DD: *laughing lightly like AG is joking* Oh AG, why are you following me around? You so kuh-razy! It's not like we can spend every second together.
Ohmuhgaw stop being silly- look HotCuteGuy is checking you out you should go talk to him! *Quick Exit!*
DD doesn't have to convince AG of anything or give her any explanation. Just tell her what the reality is: "I am going to hang out with my group, so I can't hang out with you." Friends are loyal and keep their promises. They don't intrude on each other and they give each other their space. Act like AG understands that, and hopefully she will, or at least just pretend she does!