Hamlet
You're conflicted, and you need certainty. You have to prove to yourself that Claudius really did murder your father before you act.
Now, how to determine your uncle's guilt... Claudius, the shifty man he is, has probably covered his tracks very well. It's his expertise. You don't know if questioning guards and servants on duty would turn up anything useful. The same goes for trying to tempt him into making a mistake in the future.
Perhaps what you need is something that will shatter his mask. Shake everyone to the core - Claudius, your mother, and all of Claudius's toadies...
Now, how to determine your uncle's guilt... Claudius, the shifty man he is, has probably covered his tracks very well. It's his expertise. You don't know if questioning guards and servants on duty would turn up anything useful. The same goes for trying to tempt him into making a mistake in the future.
Perhaps what you need is something that will shatter his mask. Shake everyone to the core - Claudius, your mother, and all of Claudius's toadies...