When Dolores is young, she straight-up doesn't like her Grandma, and we're not sure why. Maybe because Grandma complains all the time, about everything from how Dolores is raised to how characters act on television. Hmm… maybe this is where Dolores gets her tendency to dislike almost everything.
After Ma has her nervous breakdown, Dolores moves in with Grandma. Grandma is pretty chilly and distant, only warming up to her tenant, Jack, who ends up being a terrible rapist. When Ma dies in the tollbooth accident, Grandma cleans and remodels the house to cope with her grief. And this is important.
See, Grandma he may be cold, but she's able to hold herself together in the face of considerable tragedy, multiple times. Bernice isn't the only child she lost—her son, Eddie, drowned when Dolores was only a baby. So Grandma's ability to rally herself is not only impressive in the face of so much sadness, but also makes her pretty unique in this book. Her daughter and granddaughter are prone to falling apart. Dolores could definitely learn a little something about coping with grief from Grandma.
Once Dolores goes to college, Grandma is absent for a few hundred pages. Only when Dolores shacks up (Grandma's phrase, not ours) with Dante does Dolores contact her again. Dolores is hungry, not for Big Macs and Twinkies this time, but for information about the past. Grandma, however, wants to avoid the past like the plague.
Grandma is super racist, calling Ma's boyfriend "Mario Pepperoni" and saying that "Eyetalians [are] one step up from the coloreds" (4.143). But when she comes to Dolores and Dante's wedding, she has a strange no-more-racism Archie Bunker moment when she accidentally touches a black person's hair and realizes that it's soft (22.148). Just like that, Grandma realizes that people are just people. Or something like that, anyway.
Soon after she's miraculously cured of racism, Grandma dies. She leaves her house to Dolores, which proves that even though she wasn't the warmest and fuzziest grandma of them all (oh Grandma, what emotional disconnect you have!), she always did want to take care of Dolores.