Even though Lorelai only asked her mother to join her as revenge for nagging her to get more involved at Chilton (and perhaps even as a callback to the imaginary mother-daughter talent show at Chilton Emily teased Lorelai with in Paris is Burning), Emily actually ends up having a good time (and dare I say it, so does Lorelai? Notice how she begins smiling and having fun once she sees Luke enjoying her performance).
Lorelai and Rory so seldom allow Emily to join them in social activities, but when they do, she often enjoys being part of the fun. There’s a playful side to Emily that is rarely given the chance to come out, and that Lorelai and Rory could have really helped with if they had bothered.
The Annotated Gilmore Girls 