In Karen Cushman's novel The Midwife's Apprentice, is Alyce both the protagonist and antagonist?

No, Alyce is not the protagonist and antagonist at the same time. Alyce is the protagonist of The Midwife's Apprentice.

An antagonist is a character that stands opposed to or in conflict with the protagonist. A protagonist is the leading character in a story. A protagonist is often described as the story's hero.

Using the above definition, Jane is the story's antagonist. Readers are wanting Alyce to find success, and Jane deliberately works against helping Alyce achieve...

No, Alyce is not the protagonist and antagonist at the same time. Alyce is the protagonist of The Midwife's Apprentice.

An antagonist is a character that stands opposed to or in conflict with the protagonist. A protagonist is the leading character in a story. A protagonist is often described as the story's hero.

Using the above definition, Jane is the story's antagonist. Readers are wanting Alyce to find success, and Jane deliberately works against helping Alyce achieve her full potential. Jane constantly keeps vital midwife knowledge from Alyce. That prevents Alyce from ever being a threat to her business. Jane is flat-out antagonistic in her treatment of Alyce.

A fairly simple way to identify a story's protagonist is to ask who the story is mainly about. A reader isn't likely to say that The Midwife's Apprentice is about Jane and her servant. A reader would say that the book is about Alyce's journey to become a midwife and her struggles with Jane. Alyce is the story's hero character who struggles with various types of conflict in order to bring the story to its resolution. Between Alyce and Jane, Alyce is the "good guy." That makes her the protagonist.