No matter how horrible the acts Barbie commits, Joy is never blamed for them. This is because Joy is a powerful goddess in the form of a young girl and nobody wants to scold the being that can cause earth-shattering quakes simply by throwing a tantrum or cause hurricanes by pouting.
Subverted: Barbie tries to frame Joy and Joy immediately gets caught for it...
Double Subverted: ...but actually nobody does care anyway! Bob pulled Joy off for unrelated reasons, probably to look at his latest piece of yard art.
Parodied: It turns out Joy has done the same thing to Barbie, at the same time, and they both have the same problem. Barbie turns in Joy, but Joys parents think Barbie disguised as Joy is Joy and take her to a mental institution because they think she is a Third-Person Person.
Zig Zagged: Barbie fails to get into trouble with some people, but manages to really upset others, and she keeps working at it to try and piss off everyone so that poor innocent Joy will take all the flack. But then, at the very end, someone reveals that they knew it was Barbie the whole time, and tells the others, so that she finds that she's really in trouble for everything she did...
Averted: Barbie tries to frame Joy, but it's Barbie who gets caught and punished.
Enforced: The producers think that this kind of situation is comedy gold, and insist that it be used whenever possible.
Lampshaded: After the fact, Barbie exclaims, "Aw, c'mon! Even the most lenient parent should punish her for that!"
Invoked: Joy, realizing what Barbie is up to, goes out of her way to think of a good way to downplay the event, or immediately counteract it.
Exploited: Realizing she's an absolute Karma Houdini, Barbie starts robbing banks in broad daylight without a mask.
Defied: Barbie tries to frame Joy for misdeeds, but then before the act she realizes that it would never work because she could easily be caught on the scene of the crime. She plots to harm Joy in other ways.
Discussed: Barbie and her henchman Ken make a plan to frame Joy. Ken interjects, however, calling it a silly idea and that it is too dangerous because Barbie could be caught instead.
Conversed: Barbie, enacting her plan, snickers, "I saw this on TV once!"
Deconstructed: Barbie and Joy are just products of neglecting parents who don't care what they do, no matter how horrible.
Reconstructed: Barbie's plans are counteracted by Joy's own Evil Plan to make all the crimes and misdeeds seem like minor things not worthy of note.
Played For Laughs: Barbie goes through dozens of zany hijinks from stealing cookies to blowing up the moon just to try and get Joy into trouble, but each event is met with indifference or even praise for Joy. This raises Joy up to a near godlike level of perfection in everyone else's eyes, Barbie's plans backfiring in the most hilarious ways possible.
Played For Drama: Even though everyone is indifferent, Barbie stoops to such a horrible, insidious act, like murdering and gutting the cat, that she, and possibly Joy, are scarred for life. Neither of them will never personally live this event down, and it haunts them far into adulthood, having to attend therapy to deal with this atrocious scar on an otherwise spotless childhood.