"Stop gawking at yourself. Who are you? You think you're so pretty?" (1)
Connie's mother doesn't seem too interested in Connie's self-esteem. Maybe she is jealous and feels the need to take her down a notch.
[B]ut now her looks were gone and that was why she was always after Connie. (1)
This passage suggests a tragic rivalry between mother and daughter, when they should be friends.
Connie's mother kept picking at her until Connie wished her mother was dead and she herself was dead and it was all over. (3)
A weird parallel is suggested here between Connie's mother and Arnold, between the family structure and sexual violence. Connie's mother's "picking" kills off, psychologically, Connie's very desire to live, in much the same way that Arnold's constant badgering convinces Connie to leave with him at the end of the story.
[Her] sister was so plain and chunky and steady that Connie had to hear her praised all the time – by her mother and her mother's sisters. (3)
As in the second quote above, there's an opportunity for friendship within the family, here between Connie and her sister, that is lost in their rivalry and hostility.
Their father was away at work most of the time. [...] He didn't bother talking much to them. (3)
Connie's father is virtually invisible and mute. Lacking a real relationship with him, her only interactions with males will be with the boys she meets at the drive-in.
The father of Connie's best girl friend drove the girls three miles to town [...] and when he came to pick them up again at eleven he never bothered to ask what they had done. (5)
Like Connie's father, Connie's friend's father is detached and uninvolved. He even seems to enable the girls' misbehavior by driving them to the plaza.
Her mother went scuffling around the house in old bathroom slippers [...] (11)
Connie's mother is an image of the future Connie doesn't want – the life of a domestic housewife.
[Connie and her mother] kept up a pretense of exasperation, a sense that they were tugging and struggling over something of little value to either of them. Sometimes, over coffee, they were almost friends, but something would come up – some vexation that was like a fly buzzing suddenly around their heads – and their faces went hard with contempt. (11)
Connie has a love-hate relationship with her mother, with whom she identifies (her mother was once pretty too) but at the same time she has to distance herself from her mother in order to establish her independence. Compare as well the image we get here of their "faces hard with contempt" and the later description of Arnold's face as a "mask."
"If my father comes and sees you –"
"He ain't coming. He's at a barbecue [...] Yeah. Sitting around. There's your sister in a blue dress, huh? And high heels, the poor sad b**** – nothing like you, sweetheart!" (95-98)
Connie can't seek the protection of her father or her family now. Arnold's ironic image of a typical family barbecue makes the family seem fragile in the face of his violence.
"[...] now they're eating corn and hot dogs cooked to bursting over an outdoor fire, and they don't know one thing about you and never did and honey, you're better than them because not a one of them would have done this for you." (159)
In a way, Arnold is right. Connie's family doesn't seem to know or appreciate her, and it's doubtful from what we know about them whether they would be willing to make the same sacrifice for her.