Analyze the first part of Gertrude and Hamlet’s interview. What goes wrong (even before Polonius's death)? Who controls the conversation? Why does Gertrude call for help?

The showdown between Hamlet and Gertrude in act 3, scene 4 is pretty fraught right from the start. Gertrude starts by confronting Hamlet over his disrespectful behavior towards Claudius. But Hamlet is not in the mood for taking lectures in disrespect from his mother. As far as he's concerned, it is she who has been disrespectful to her late husband, Hamlet's father, by marrying the usurper Claudius and sharing his bed. Hamlet is so infuriated by what he perceives as Gertrude's shameless audacity that he tells her to her face that he wishes she weren't his mother:

You are the queen, your husband’s brother’s wife, And—would it were not so!—you are my mother.

Gertrude is supposed to be controlling the conversation. Polonius has given her precise instructions that she should give Hamlet a serious dressing down over his recent behavior. Yet it is Hamlet who quickly dominates the brief, acrimonious slanging match that ensues. His language is so violent, his manner so intemperate, that Gertrude rapidly loses control of the situation, her parental authority completely undermined by Hamlet's willful disobedience. Gertrude wants to leave, but Hamlet forces her to stay put. At this point, Hamlet's behavior is so disturbing that Gertrude thinks her son is about to kill her:

What wilt thou do? Thou wilt not murder me? Help, help, ho!