What is learned of the relationship between Elizabeth and John from the opening dialogue and stage action of Act Two in The Crucible? no
The opening conversation between Elizabeth and John in Act II, scene i, shows that they are very tense and uncomfortable around each other. They are both trying to be on their best behavior, using very civil words and making polite small talk, but they are not conversing in a very warm or loving manner.
When John comes in from planting, the reader quickly learns that Elizabeth has been nervous about where he has been, stating he "come so late (she) thought (he'd) gone to Salem this afternoon." Elizabeth is still feeling suspicious of John's actions, knowing not so long ago he had an affair with Abigail, and even though he has told her the affair is over, she has a hard time trusting him.
She is also nervous about the events going on in town since she has learned that Abigail is behind many of the accusations of witchcraft and that there are now 14 people in jail. She tells her husband:
"The Deputy Governor promise hangin' if they'll not confess, John. The town's gone wild, I think. (Mary Warren) speak of Abigail, and I thought she were a saint, to hear her. Abigail brings the other girls into the court, and where she walks the crowd will part like the sea for Israel."
Elizabeth recognizes the power Abigail has, and perhaps is already worrying whether Abigail might try to use that power against her. She also seems to wonder if Abigail still holds any power over her husband. When John says of Abigail's behavior in court that "it is a black mischief," Elizabeth urges him to let the court know Abigail is a fraud.
John, however, holds back - his own guilt at this point paralyzing him. When he tells Elizabeth he will "think on" whether to tell the court that Abigail told him the earlier scene in the forest "had naught to do with witchcraft," Elizabeth pushes him to speak up. John must now admit to her that Abigail said this "to (him) in a room alone - (he has) no proof for it."
In saying this, he has to admit to Elizabeth he lied to her when he said he had not been alone in town with Abigail. This raises her suspicions once again, and as the stage notes reveal, "she has suddenly lost all faith in him." Her suspicions anger John, who says he is tired of her inability to forgive and forget, as well as of her constant judgment and coldness. He urges her:
"Learn charity, woman. I have gone tiptoe in this house all seven month since she is gone. I have not gone from here to there without I think to please you, and still an everlasting funeral marches round your heart. I cannot speak but I am doubted, every moment judged for lies, as though I come into a court when I come into this house.... I'll plead my honesty no more, Elizabeth."
Clearly, John is tired of having to defend himself. Elizabeth claims she does not judge him - "the magistrate sits in (his) heart that judges (him)" - but even if that is true, John FEELS judged, and their relationship is on thin ice as the play begins.