Mrs. Shales (Meagen Fay) tells Lorelai that her daughters, twins Jackie and Jessica (Kelly and Ashley Cohen), were spoiled by their father. As a result, she can barely stand the sight of them, and is sick and tired of their quarrelling.
This provides an example to Lorelai of what could go wrong with her relationship with Rory: she could become spoiled by her wealthy grandparents to the point that it affects her relationship with Lorelai. It helps feed Lorelai’s fears during the episode.