What is the conflict inside Hamlet after his father's sudden death, his mother's marriage to his uncle?
Well, for one thing, Hamlet's father is gone. Hamlet didn't get a chance to say goodbye, and he is in a deep moment of grief and loss. He is suffering the loss of a parent, and you are really never old enough to be ready for this sort of loss. His grief is fresh and severe.
For another, he states that the "funeral meats were used on the wedding table". The marriage happens too quickly. A funeral is a time for mourning, and a wedding is a joyous occasion. How can something so happy happen when the sad mood still lingers? Not to mention--yuck!--she has married his father's brother. Now you put yourself in those shoes. How would you feel if your father died suddenly and your mother married your uncle within days of the event?
Further, Hamlet does not believe his mother has grieved sufficiently for his father, her original husband. If he is still grieving, why isn't she? He can't understand it...instead, she is flitting around with a giddy smile on her face because she has a new husband...one who reminds her so much of the old one that it's like nothing ever went wrong.
This is why, later in the play, Hamlet states that "Frailty's name is woman" because it almost seems as though his mother can not survive without being married to someone. That her identity is tied to the man with whom she shares a ring, a name, a vow, and a bedroom.