This 1994 television movie directed by Oz Scott is the movie Lorelai and Rory watch with Dean. It has been previously mentioned as a biographical drama film in which Joan and Melissa Rivers played themselves, recreating key moments in their lives together.
Lorelai mentions some of these, such as the suicide of Melissa’s father, Edgar Rosenberg in 1987; Joan getting banned from The Tonight Show, where she first became famous, in 1986 (she didn’t return until 2014); and Joan forcing Melissa to get a nose job at eighteen which matched her mother’s nose job around 1986.
The film was panned as critics as strange, embarassing and self-indulgent, so Lorelai and Rory are not alone in mocking it. I would imagine they are watching a video of the movie which Lorelai taped off TV.
Rory has just got back with Dean, and he is immediately returned to the status quo of watching movies chosen by his girlfriend and her mother, and doing chores for Lorelai. I guess we’re meant to assume that just being permitted to love a Gilmore girl is so wonderful that you will allow yourself to be treated like a nonentity in sheer gratitude.