To Be or Not to Be an Agent of God?

Hamlet believed that his actions were all to be viewed as righteous for he was an "agent of God". He feels that in order to avenge his father's murder, to hell with those that get hurt in the process. He felt no remorse for killing Polonius, granted we dont really know whether or not he liked the man, but if you claim to love the man's daughter then surely you should feel something, no? So the question that remains is do we believe this to be true? To be or not be an agent of god?
Comparing Othello to Hamlet there are similarities and differences. Both Othello and Hamlet feel that they are murdering to bring about justice for a wrong commited. i dont recall however, that Othello ever considered himself and intrument of god. His reason for murdering Desdemona was because she was unfaithful and because he wanted to "save other men" from her decieving ways. Hamlet on the other hand was looking to avenge his father so that his soul may rest in peace but to me it seemed as though he simply did not like the fact that his mother choose to remarry to his uncle.
Polonius said that there was "a method" to Hamlet's maddness. Though some people could argue that he went crazy i think that to a certain extent this is true but yet to another no, he was as perfectly comprehensive. Both he and Othello sought ways to have their sinners confess or reveal their guilt. But there was no method to Othello's way of seeking the truth from his wife, he was simply a puppet in the hands of Iago the puppeteer. Hamlet on the hand is the both the puppet and the puppeteer. He recieves orders from the ghost but all of his means to get to this end were all his doing, not someone ordering him about as was the case of Othello.
At last, both Othello and Hamlet choose to murder because the loved. Yet, unlike Hamlet Othello never had any intention of hurting those around him, only the people who he thought to have hurt him, which in this case was Desdemona and Cassio. Hamlet, by "feigning" to be mad hurt the woman whom loved him, two of his good friends and an inocent man, Polonius, and he did all this without any remorse.
So, was he or was he not an agent of god? In my honest opinion he's just a sad murderer.