Just about every scee shows some form of relationship. You want to concentrate on:
Claudius-Gertrude-Hamlet
Hamlet-Ophelia
Hamlet-Claudius
Claudius-HamletSnr
Gertrude-Hamlet (Oedipus complex? O.O)
These are all good r'ships to consider as they can all be equally discussed along with other themes/etc. Desire, incest, misogyny, betrayal, vengeance, etcetc.
As for whereabouts they are strongest in the play..
Claudius-Gerty-Hamlet = probably court scene in Act 1? :|
Hamlet-Ophelia = various times when they are together, perhaps the moment when he rejects her or later when she goes "mad"?
Hamlet-Claudius = the chapel - love this soliloquy!
HamletSnr-Claudius = hunt down the moments where C is lamenting his brother's tragic untimely passing (cracks me up every time), I think it's the court scene in act one again.. and also the moment the ghost reveals to HJnr that C killed him (HSnr). Stress the point that they were brothers and now C has killed HSnr, stolen his throne and married his wife. :O
Gerty-Hamlet = once again, the scene escapes me (dammit) but just read the text again and you'll figure it out.. <- Oedipus complex!? Gasp.
Good luck with your Hammie!