You really don't want to cross Elaine Miller. She'll lecture you to death.
Elaine is William's mother, a college professor with a knack for calling 'em how she sees 'em. She is an intellectual, she's fiercely independent, and she makes it absolutely clear which elements of society she deems immoral. This list includes—but is certainly not limited to—rock and roll, which she does not allow in her home. This environment is simply too stifling for Anita, who cannot stand her mother's restrictions and her preferential treatment of the precocious William.
Elaine's dream for William is that he will become a lawyer, and she gets pretty bent out of shape about his new-found passion for rock writing. But she manages, nonetheless, to support him the best she can. Though William probably hears her mantra of "don't take drugs" in his sleep, it's clear that Elaine cares deeply about her son and will do her darnedest to keep him on the path to success. She already lost one child—she would be devastated if it happened again.
Eventually, however, Elaine realizes that rock writing is, in fact, William's dream. She wanted her kids to succeed on her terms, at the expense of their own passions and aspirations, and that's what drove her daughter away. When Elaine and Anita reunite at the end of the film, each woman understands that the other was just doing the best they could. They just needed a bit of distance and time to see.
In the end, William and Anita turn out to be extremely independent, intelligent, and passionate individuals—just like their mother. Though she can be overbearing at times, Elaine always shows tremendous love for her kids. Her goal is to help them become the best human beings they can be, by equipping them with the substance and rectitude to navigate what she sees as an increasingly immoral world.
We think, ultimately, she succeeded.