In "Young Goodman Brown", how does Goodman Brown view his action in relation to his family history?
You have asked two questions so I have had to edit it down to only one, according to enotes regulations. Like so many of Hawthorne's short tales, this story is rich in allegorical overtones, in that it is clear that the characters and actions stand for abstract qualities. As Goodman Brown sets off on his journey into the woods, a "fellow-traveller" journeys with him, who it is clear is the Devil. The journey into the forest itself has allegorical significance, as is made clear when Goodman Brown responds to the invitation of the Devil to go deeper into the woods:
"Too far, too far!" exclaimed the goodman, unconsciously resuming his walk. "My father never went into the woods on such an errand, nor his father before him. We have been a race of honest men and good Christians since the days of the martyrs; and shall I be the first of the name of Brown that ever took this path and kept-"
It is clear then that Goodman Brown is proud and convinced of his own "goodness", as represented by his name, for he, in his own imaginings, at least, is a "good man." The journey into the woods, therefore, is representative of engaging with evil. However, note how the Devil responds to this protestation of goodness:
"Such company, thou wouldst say," observed the elder person, interpreting his pause. "Well said, Goodman Brown! I have been as well acquainted with your family as with ever a one among the Puritans; and that's no trifle to say. I helped you grandfather, the constable, when he lashed the Quaker woman so smartly through the streets of Salem; and it was I that brought your father a pitch-pine knot, kindled at my own hearth, to set fire to an Indian village, in King Philip's war. They were my good friends, both; and many a pleasant walk have we had along this path, and returned merrily after midnight. I would fain be friends with you for their sake."
Key to this story, and so many of Hawthorne's tales, is the idea of the darkness of humanity, however sinless it pretends to be. Hawthorne makes it clear that sin touches everyone, including the supposedly "Goodman" Brown. You might find it interesting to compare this short tale to another one of Hawthorne's gems: "The Minister's Black Veil", which likewise touches on this theme of the universal sinfulness of humanity.
There is quite a bit of irony to be read at those references to Goodman Brown's family members. Brown believes that he comes from a long line of faithful and upstanding citizens of the Puritan community and the Devil agrees and brings up two examples examples. He says, "I helped your grandfather, the constable, when he lashed the Quaker woman so smartly throught the streets of Salam." To Brown's ears, the actions of his grandfather are good because Quakers were not of the truth faith and needed to be punished for their practice of their varient religious beliefs. But we as readers recognize that Hawthorne is illustrating the narrow-minded and cruel behavior of the Puritans.
The second example the Devil mentions is that it was he that "brought your father a pitch-pine knot, kindled in my own hearth, to set fire to an Indian village." Again, Brown sees his father's action against the innocent Indians as an appropriate thing because the heathen Indians were "bad," but Hawthorne is again illustrating the irony of these people's actions. In the name of supposed good, they are doing evil. Man is prepetually tempted into sinful behavior, frequently at the behest of "doing the right thing."
Understanding Hawthorne's tone and his rhetorical stance are vital to a clear understanding of his stories.