It is also very possible that up to this point in the play, Gertrude has been completely innocent of the real reason her husband, King Hamlet, has died. Since there was no CSI in this time period, his death in the garden appears to have a natural cause behind it. When young Hamlet speaks to his mother in her bedchamber he raises questions regarding the too quick marriage of his mother to his uncle-father and plants the seed that perhaps Claudius has planned this all the while by murdering the former King. With all this in mind, it stands to reason that Gertrude does not tell Claudius what young Hamlet's plans are not only because she has told him she won't, but also because she is uncertain of Claudius now. What is to keep him from murdering again? In fact, we, the reader, know that he has been planning all along to murder young Hamlet as well. So, with all this in mind, it stands to reason that Gertrude probably fears her current husband and his intent, and so keeps young Hamlet's counsel.
Hamlet tells his mother of his plans because he trusts his mother. Also, the ghost of his father has appeared to him again and it reminds Hamlet of Hamlet's purpose: at avenge his father's death, not to harm his mother. The ghost tells Hamlet to speak to her (Act 3, sc. 4), so Hamlet does and he tells her what his plan is. Hamlet also tells his mother here not to have anything more to do with Claudius. Gertrude doesn't tell Claudius because she has told Hamlet that she won't. Also, it is possible that Gertrude really does believe that Hamlet is mad.