Act 2 Personal Reaction-Tori

I thought it was interesting how King Claudius acts when the sanity of Hamlet is questioned.  I think that he doesn't trust Hamlet, and knows that Hamlet is cunning and intelligent enough to uncover the truth of King Hamlet's death, therefore he feels that he must do whatever is necessary in order to label Hamlet as a "lunatic."  I also find it strange that Polonius feels that it is necessary to make up a lie about Hamlet writing a love letter to Ophelia.  I don't understand what good that this would do for him or anyone else for that matter.  When the Queen, Rosencrantz, and Guildenstrern do not stand up for Hamlet against the ambassadors, the King, and Polonuis I start to question their loyalties, and their character for they seem to either have no loyalty, or they feel that they have no choice in the matter.