What are the conflicts in which Hamlet's or Ophelia's minds are pulled into different directions? Are there any quotes in the play that show...

The entire play could be considered proof of Hamlet's uncertainty.  Throughout the play, he feels pulled in different directions.  He wants to believe the ghost and avenge his father's murder, but he continues to think about it rather than act on it which leads to his frustration with himself and his inactivity.  During the play, he considers the ramifications of avenging the murder - the fact that he'd have to commit murder which is wrong, for example.   Hamlet's soliloquy in Act 3, sc. 1 is one long example quotation displaying Hamlet's uncertainty.  He expresses the idea, in this speech, that he's tired of bearing the burdens of life and all of its stresses - namely here, the death of his father and the subsequent hasty remarriage of his mother to his uncle - but goes on to say that killing oneself is a sin, plus no one knows what death is like so it might be worse than life.  He goes on to lament the fact that this uncertainty is what stymies people and keeps them from killing themselves.  A good example of Ophelia being pulled in different directions comes in Act 1, sc. 3, when she reluctantly tells her father of her relationship with Hamlet.  She does not want to disobey her father, but it's clear she cares for Hamlet.  She tells her father that she will obey him when he tells her to stop seeing Hamlet, but it's especially clear in Act 3, sc. 1 when she and Hamlet talk that she is not happy about having complied.