How has the relationship between Macbeth and his wife changed since the death of Duncan? Why aren't they happy?
At the beginning of act 3, scene 1, we see that Macbeth has begun to arrange for two murderers to kill his former best friend, Banquo, and Banquo's son, Fleance, as they are on the road, away from home. In a soliloquy, before the murderers arrive, Macbeth reveals why he wants Banquo dead:
Upon my head [the Weird Sisters] placed a fruitless crown
And put a barren scepter in my grip,
Thence to be wrenched with an unlineal hand,
No son of mine succeeding. If 't be so,
For Banquo's issue have I filed my mind:
For them the gracious Duncan have I murdered . . . (3.1.66-71)
He is angry, then, that he will not pass his crown to his own children and that Banquo's descendants will, according to the three Weird Sisters, be kings. He is unhappy and he doesn't feel secure in his power because he knows, at some point, that power will pass to Banquo's kin instead of his own. He even says, "To be thus is nothing, / But to be safely thus" (3.1.52-53). He means that it is not good enough to be king, but he must feel safe and secure in his position. He is quite unhappy that he lacks this security and plots to achieve it.
In the next scene, when Lady Macbeth is alone, she says,
Naught's had, all's spent
Where our desire is got without content.
'Tis safer to be that which we destroy
Than by destruction dwell in doubtful joy. (3.2.6-9)
She is sad and frustrated because she and Macbeth have achieved what they set out to when they plotted Duncan's murder—they are king and queen now—and yet they are not happy because they feel only a "doubtful joy." Because they fear for their security, they cannot really be happy.
Furthermore, Macbeth has begun to act without consulting her, without even telling her about his plans. They used to be "partners" and now they are not; Lady Macbeth used to make decisions, and now Macbeth makes them all on his own, creating a rift in their relationship. At the end of the scene, when she does ask what he's planning, he tells her,
Be innocent of the knowledge . . .
Till thou applaud the deed. (3.2.51-52)
In other words, he flat out says that he isn't going to tell her; he wants her not to know until she can congratulate him. He even tells her how to behave toward Banquo at their party that night despite the fact that he plans for Banquo never to come. Macbeth lies to her, and she does not like being kept in the dark.
Actually, their relationship changes before King Duncan's murder. When Macbeth becomes Thane of Cawdor and begins to believe in the witches' prophecy, he writes to Lady Macbeth telling her his amazing news. The audience does not see Macbeth write the letter, but Scene Five begins with Lady Macbeth's reading it aloud. Macbeth's words make it clear he has embraced the prophecy. He calls her "my dearest partner of greatness" and speaks of their "rejoicing." Lady Macbeth's reaction to the letter shows that she and Macbeth share a strong desire for the crown. This is the last time they commune in harmony.
When Macbeth learns of his wife's murderous plans, he first puts them aside, telling her "We will speak further." When he tells her planning to murder Duncan will stop, she attacks him vehemently, even questioning his manhood. She grabs power in their relationship at that point and maintains it until her own emotional unraveling in Act Five. Thus, Macbeth's most tender feelings for his wife are destroyed early in the drama. He sees her as both incredibly cruel and unwomanly. Ironically, his tenderness toward her revives when her guilt destroys her.
Once crowned, Macbeth and his wife cannot enjoy their power; they guard it jealously. Macbeth kills Banquo to prevent Banquo's portion of the witches' prophecy from coming true, that his heirs would rule. Fleance's escape, however, makes Banquo's murder pointless. Murder follows murder until the final destruction of Macbeth and Lady Macbeth.