Gertrude is a loving mother who wants her son to be happy and to accept her marriage to Claudius (Act 1, sc. 2, ll. 68-73). She is worried about her son and his mindset because she knows he loved his father and is grieving about his death. She is so worried about his mental state that in Act 2, she and Claudius send for Rosencrantz and Guildenstern to try to find out if there is anything more bothering Hamlet (Act 2, sc. 2, ll. 19-26).
Ophelia is an innocent and dutiful daughter. When her father asks her to stop seeing Hamlet, she obeys his request (Act 1, sc. 3, l.137). More proof that Ophelia is a good, dutiful daughter is seen in Act 2 when Polonius reads to Claudius and Gertrude a letter Hamlet sent to Ophelia. It is clear that Ophelia has turned over to her father the love notes Hamlet sent to her (Act 2, sc. 2, ll. 115-128).
Claudius wants to get on with his real passions - ruling Denmark and being Gertrude's husband. In Act 1, sc. 2, in his opening dialogue and in the long dialogue addressed to Hamlet in ll. 87-117, Claudius quickly deals with the subject of his marriage to his former sister-in-law and very quickly moves on to dealing with the Fortinbras/Norway problem. When he talks to Hamlet, he gently chastises him for mourning his father to the extent that he does. Claudius wants to move on past the death of his brother because, as the murderer, he doesn't want King Hamlet's death to be an issue. This desire for Hamlet's problem to be something other than his father's death carries on to Act 2 when Polonius says that he thinks Hamlet's problem to be unrequited love. Polonius says that Ophelia broke off her relationship with Hamlet and that has caused Hamlet's depression.