Family is a significant theme in Hamlet. The play is notorious for the way it dwells on the issue of incest – Gertrude's marriage to her dead husband's brother, Hamlet's fixation on his mother, and even Laertes's obsession with Ophelia's sexuality. It's also important to note how the play is particularly concerned with the way politics impact the dynamics of family relationships, especially when domestic harmony is sacrificed for political gain. Also of importance is the fact that Hamlet involves three revenge plots that all hinge on sons avenging the deaths of their fathers.
In Hamlet, parents cannot be trusted to care for their children, especially when matters of politics are involved.
Hamlet grieves for the loss of his father but it seems that his mother's marriage to Claudius is more upsetting to Hamlet than anything else.