What does Miller want the audience to understand about John and Elizabeth Proctor's relationship in Act Two?

In Act Two, Miller wants the audience to understand the dynamics of the conflict between Elizabeth and Proctor. There is tension in the relationship because Elizabeth finds it difficult to forgive Proctor for his adulterous romance with Abigail Williams.

Each encounter between the two is fraught with emotion and suspicion. Meanwhile, Proctor finds that he must constantly defer to his wife in all things. His pitiful and almost groveling "I mean to please you" assertions only demean him in Elizabeth's eyes. Despite all his efforts, Elizabeth still distrusts him greatly. When he is late coming home, she accuses him of having gone to Salem. However, she later perversely begs him to go to Salem to denounce Abigail and to proclaim to the officials that all her accusations about witchcraft are lies.

In Act Two, it is clear that, even though Elizabeth and Proctor are discussing the witch trials, there is a deeper conflict going on; the surface discussion masks an underlying tension between Proctor and Elizabeth. From Elizabeth's viewpoint, Proctor's continuing interactions with Abigail is unforgivable. Elizabeth is further incensed when she discovers that Abigail was alone with Proctor when she told him the truth about the accusations. Elizabeth thinks that Proctor still harbors lustful feelings for Abigail, and her violent feelings of anger inhibit all of Proctor's efforts at reconciliation.

Elizabeth accuses Proctor of not wanting to go to Salem because he is afraid; she asserts that he hesitates because it is Abigail he must denounce. Upon hearing this, Proctor loses his temper. He maintains that he's tired of living like a criminal, and he unleashes his own brand of anger upon Elizabeth:

PROCTOR: Spare me! You forget nothin' and forgive nothin'. Learn charity, woman. I have gone tiptoe in this house all seven month since she is gone. I have not moved from there 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!

For her part, Elizabeth argues that Proctor has not been forthcoming with her. Basically, she thinks that Proctor has neglected to earn back her trust. Meanwhile, Proctor laments his foolishness in confessing his infidelities to his wife. Elizabeth argues that she has a right to worry: Abigail only condemns her because she wants to reunite with Proctor.

Elizabeth presses her husband to expose Abigail as a whore and to break whatever promises he made to her. Proctor is incredulous that his wife still thinks he has designs on Abigail. To Proctor, the affair with Abigail was all about physical pleasure, nothing more. So, he can't understand or relate to Elizabeth's current fears.

PROCTOR: Woman, am I so base? Do you truly think me base?
ELIZABETH: I never called you base.
PROCTOR: Then how do you charge me with such a promise? The promise that a stallion gives a mare I gave that girl!
ELIZABETH: Then why do you anger with me when I bid you break it?
PROCTOR: Because it speaks deceit, and I am honest! But I'll plead no more! I see now your spirit twists around the single error of my life, and I will never tear it free!
ELIZABETH, crying out: You'll tear it free—when you come to know that I will be your only wife, or no wife at all! She has an arrow in you yet, John Proctor, and you know it well!

In Act Two, Miller wants us to understand that the relationship between Proctor and Elizabeth is doomed to irreconcilable conflict so long as Abigail still has her "arrow" in Proctor. Basically, Abigail's interpretation of the affair is opposed to Proctor's. While he thinks of her as a passing fancy, Abigail thinks of Proctor as something more. Her obsession with Proctor is largely what inspires her venom against Elizabeth and what threatens the couple's marriage.