In Shakespeare's Hamlet, Gertrude does, indeed, do exactly as Hamlet asks her to by telling Claudius that Hamlet is as mad as the wind and sea when they contend, etc. And she certainly could be demonstrating loyalty to her son and attempting to protect him. Hamlet gives her a direct order, and she does as he orders.
At the same time, one should be aware of another way of interpreting her behavior and words. In short, Gertrude may tell Claudius that Hamlet is mad, because she thinks he is mad--and one could hardly blame her.
Look at Hamlet's behavior and words while he's alone with his mother in Act 3.4:
- He is so aggressive toward her that she thinks he's going to hurt her and she cries for help: "What wilt thou do? Thou wilt not murder me?/Help, ho!"
- He kills Polonius, thinking it is the king, for hiding behind the arras and listening in.
- Sees a ghost.
- Repeatedly harps on Gertrude's sex life. Hamlet seems...
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