Alternative idea: if at any point during the first round of parties she is asked why she is going through recruitment, she can say something to the effect of "Well, my older biological sister is an XYZ, but we're very different people and I'm interested in finding my own sorority home that I can love as much as she does hers." Gets the point across without sounding too forced or obnoxious. Best of luck to your daughter!

Clemsongirl, you are wise beyond your years!