John cheated on Elizabeth with Abigail and it is Abigail who starts the witchery and the hunt against Elizabeth. The girls are accused of dancing and chanting in the woods and they were doing it because Abigail wants a spell or charm to make John leave Elizabeth. Once caught Abigail is the catalyst for Rev. Hale looking at J and E's home for witchcraft. She even plants evidence.
I would say that this is a secondary plot line as the whole play is symbolic of the McCarthy hearings in the US at the time Miller wrote this. Though the story of J and E is quite a love story.
John pointedly says that Elizabeth does not lie, yet when in custody she lies to try and save John's good name, thus condemning to be hanged as he refuses to admit to being a witch and sign a paper to that effect. He dies to save his name and for the protection of that name for his children.
Their relationship and its shortcomings does drive the play when I look at it from this question.
I love this play and teach to my 11th graders every chance I get. Would love to see some of the assignments given by your daughter's teacher.