I don't know any teenager - then or now - that would invite someone who wasn't their friend to be apart of their group at prom just to be nice. Ok, I'm sure that somewhere, some selfless teen as done so, but really, it's not something that happens. Nor, frankly, should it.
Prom is certainly a rite of passage of high school. BUT, it is not a RIGHT. One does not have to go to prom. Most kids want to, but that doesn't mean they get to. The cost may be too much, one may not have a date, one may not have any friends, and/or one may not want to go completely alone. All that is sad, but, honestly, just too bad.
Where I grew up, the prom was for juniors and seniors. So, potentially, you could go both years. And, actually, since a junior or senior could take anyone, you could potentially go 4 or 5 years to the prom. I, oddly enough since I was generally a bit of a misfit, went to several proms. I went to another school's prom as a date when I was a freshman. I went to my junior prom with a long-time family friend. I went to a another school's prom with a good friend our senior year and to my own senior prom alone. I did go to another senior prom with a guy who liked me. That was my "good deed". I went with him so he could go to his prom. However, nice as I was, I would have never taken someone I didn't like to my own prom just to be nice to them. I don't know anyone who would have.
Also observed at these 5 proms I attended, it was nothing like the group love mixer some posters are described. There was generally fairly little mixing between groups. You hung out with the group you came with or your closest friends that you met up with after dinner. (Dinner was separate and generally done as a pair or as a double date). You may say hello to others or chat briefly but in general everyone was enjoying being with their own crowd. Frankly, there really wasn't any room for a lone prom goer to insert herself into any given group. (When I went by myself, I didn't even try. I respected my friends with their dates too much. I just wanted to go for a short time.)
I don't see any reason why the OP's DD needs to invite AG to crash her party, either directly or indirectly. Sure, it's sad AG may not go to prom, but that is very much not the OP's DD's problem.