In the opening dialogue of Act II of Arthur Miller's The Crucible, what do you sense about John and Elizabeth Proctor's relationship?
As the other commenter notes, we get a definite sense of the strain on the relationship between John and Elizabeth Proctor in the opening pages of Act II. However, we also get a sense of how hard each of them is trying to repair the damage done to their relationship. Although we see John salt the stew Elizabeth has prepared before she comes in, when she serves him and then watches as he tastes it, he says, "It's well seasoned." We know very well that he didn't think so, because he added seasoning himself without her knowledge, but he seems to want to take the opportunity to compliment her. He doesn't want her to know that he salted it. Further, she is anxious for his approval, as is conveyed by her desire to see his reaction to the meal, and she seems to respond well to the compliment, "blushing with pleasure." She says that she "took great care," as though pleasing her husband is of paramount concern to her.
Moreover, when John mentions buying a cow from George Jacob, he asks if it would please Elizabeth, and she says that it would. "I mean to please you, Elizabeth," he says, and she responds, "I know it." John openly acknowledges his desire to please his wife; he seems to genuinely desire her forgiveness and trust again. He purposely compliments her, he consults her on important decisions regarding the farm, and so forth. She understands the overtures he's making, though it is still difficult for her, and she is trying to bridge the gap between them in her own way as well.
The relationship between John and Elizabeth, that is, their marriage, is strained from the beginning of the play. John had previously confessed his adultery with Abigail to his wife, she has fired Abigail for it, and there is bitterness and mistrust between them.
John Proctor complains of the coldness of the house she keeps, laments the absence of even some flowers on the table for color, and Elizabeth doesn't react. She keeps telling John about what is happening in the Court, silently pressuring him to do something to stop Abigail. You can tell that John at this point just wants to ignore the whole thing, ashamed of his adultery and angry that it keeps coming up. This spills out into the dialogue between them and shows us how unhappy the marriage is.