Family in Hamlet

Claudius: “But now, my cousin Hamlet and my son,” Hamlet: [Aside] “A little more than kin, and less than kind”
Claudius: “How is it that the clouds still hang on you?

”
Hamlet: “Not so, my lord; I am too much i' the sun.” Gertrude: “Good Hamlet, cast thy nighted color off”. (1.2.66-70)
Hamlet's continued mourning while Claudius is needfully desirous that Hamlet stop mourning his father's death and start celebrating his mother's new husband, the country's new King and his own new father.
“Tis sweet and commendable in your nature, Hamlet, To give these mourning duties to your father; But you must know, your father lost a father; That father lost, lost his, and the survivor bound In filial obligation for some term to do obsequious sorrow. But to perserver in obstinate condolement is a course of impious stubbornness; 'tis unmanly grief" (1.2.89-96)
Claudius telling Hamlet he is just being stubborn and should get over his father as it has been a month and the time for mourning has passed.
“A little month, or ere those shoes were old
With which she follow'd my poor father's body,
Like Niobe, all tears:--why she, even she--
O, God! a beast, that wants discourse of reason,
Would have mourn'd longer--married with my uncle,
My father's brother, but no more like my father
Than I to Hercules” (1.2.151-158)
Hamlet is frustrated with his mother and her lack of mourning for his father after his funeral. She had married Hamlet’s uncle less than a month after the funeral. Hamlet is disgusted and compares Claudius as being as much like his father as he to Hercules.
“She married. O, most wicked speed, to post
with such dexterity to incestuous sheets! It is not nor it cannot come to good:
But break, my heart; for I must hold my tongue.” (1.2.161-164)
Hamlet not only takes issue with his mother's quick remarriage after his father's death, he's also and accuses Gertrude of being guilty of "incest." The death of his father and marriage of his uncle were so close that the sheets may not have been changed.
“but you must fear,
His greatness weigh'd, his will is not his own;
For he himself is subject to his birth:
He may not, as unvalued persons do,
Carve for himself; for on his choice depends
The safety and health of this whole state;
And therefore must his choice be circumscribed
Unto the voice and yielding of that body
Whereof he is the head.” (1.3.19-27)
Laertes tells Ophelia that Hamlet can't marry who he wants to—he has to marry for the safety of the entire state and Ophelia is just entertainment for the time being until he takes the throne. Laertes insists that a marriage between Ophelia and Hamlet is impossible. Marrying for love? That was for the commoners.
“Then if he says he loves you,
It fits your wisdom so far to believe it
As he in his particular act and place
May give his saying deed; which is no further
Than the main voice of Denmark goes withal.
Then weigh what loss your honour may sustain,
If with too credent ear you list his songs,
Or lose your heart, or your chaste treasure open
To his unmaster'd opportunity.” (1.3.27-36)
Here, Laertes tells Ophelia that, if she sleeps with Hamlet, she'll lose her honor. Ophelia's chances for a future marriage could be compromised if she does.
““But if’t be he I mean, he’s very wild, addicted so and so.” and there put on him
What forgeries you please; marry, none so rank
As may dishonour him; take heed of that;
But, sir, such wanton, wild and usual slips
As are companions noted and most known
To youth and liberty.” (2.1.20-26)
Polonius spies on his kid while he's away at college. And he's not the only one. Claudius, Hamlet's step-father/uncle, also goes to great lengths to find out what Hamlet's up to.
“O, my offence is rank it smells to heaven;
It hath the primal eldest curse upon't, 
A brother's murder.” (3.3.40-43) As King Claudius prays, he acknowledges that, by murdering his brother, Old Hamlet, he has brought upon himself the oldest and first curse, which is a reference to the biblical story of Cain, who committed the first murder when he killed his brother Abel.
Gertrude: “Hamlet, thou hast thy father much offended.”
Hamlet: “Mother, you have my father much offended.” (3.4.12-13)
Ugh, mom, it’s not like he’s my real dad…