How does Miller use tension in the family to underscore Willy's character in Death of a Salesman?
One of the largely unstated tensions in the family is Happy's failure to mature and his womanizing. He is the quintessential "cad", harboring no real or deep feelings for anyone and demonstrating this through his behavior with women. The notion that this is also true of Happy in relation to his family remains implied, but is a strong undercurrent in the play.
Willy is unfaithful to Linda at one point. He does not admit this to Linda. Instead, the affair (discovered by Biff) remains a suppressed secret. Happy's flaws are similarly left un-discussed, creating a parallel between Willy and Happy.
The emotional failures of Willy are reflected in those of Happy. Happy's character, in this way, helps to articulate Willy's weaknesses as a husband and father.
Biff's professional failures stem in part from his resentment against his father and also from Willy's successful attempts to inflate Biff's ego. Willy incessantly reminds Biff that he can be great, like his uncle. Fueled by this ego-boost, Biff allows himself to be fooled into believing he is better than he really is. This inflated sense of self paves the way for Biff's entitlement and exceptionalism, leading him to petty theft and self-betrayal.
Willy can be seen as subject to the same or similar dynamics as he insists that he was once a great and beloved figure up and down New England. He is fired as he espouses this belief to his boss. He is rebuked for espousing it to Charley. He fails, in the end, because he cannot help but believe it himself.