Jack is the father of a young family. He enjoys telling tales and views regular bedtime stories with his daughter, Jo, as a creative outlet. Jack grows increasingly dissatisfied with domestic life and is upset when he finds that his stories no longer captivate his daughter like they once did.
Jo is Jack and Claire's four-year-old daughter. She is going through a "reality phase" (345) in which she questions whether concepts and claims that her parents make are real. She's starting to be able to distinguish fantasy from reality and grows less agreeable and less interested in what Jack has to say.
Claire is the mother of Bobby and Jo. She is six months pregnant with their third child. While Jack is upstairs telling Jo a story, Claire is downstairs painting the trim in the living room, a task which—as soon as he's done telling the story—Jack is expected to join her in doing. Claire, too, from the few details Updike provides, seems to take little pleasure in their domestic, suburban lives.
Roger Skunk is a fictional character invented by Jack with the help of Jo. Roger Skunk is a target of bullying at school because of his strong odor. He pays the wizard to use magic to remove his odor so that he'll be accepted at school, but when he goes home smelling, instead of like a skunk, like roses, his mother, "Mommy Skunk," forces the wizard to return his skunk smell.
Wizard is a recurring character in Jack's bedtime stories. He is often the person to whom the wise old owl refers Roger X and provides the deus ex machina that usually concludes Jack's stories.
Owl is another recurring character in Jack's stories. He's is supposed to offer Roger X some sage piece of advice, but usually just refers Roger to Wizard.
The titular "Mommy" of "Should Wizard Hit Mommy?" is actually Roger Skunk's mother (also a skunk) who forces Wizard to return Roger to his original skunk-like smell. Jo hates Mommy Skunk's function in the story and roots for her to be hit by Wizard.
Should Wizard Hit Mommy? Questions and Answers
The Question and Answer section for Should Wizard Hit Mommy? is a great
resource to ask questions, find answers, and discuss the novel.