Melancholia/WMG

The first half is real, the second half of the movie is a nightmare that Justine is having as she finally catches some sleep after the overnight wedding.
The wedding in the first part is shown to drag on forever, starting hours later than planned and lasting well into the next morning, and is a miserable experience for all involved. When the bride, exhausted and depressed, is finally able to get some sleep, she dreams the second half of the movie.

While Lars Von Trier freely states they made no attempt to get the astrophysics correct, they did a decent enough job to make Melancholia believable within "dream logic" (i.e. You accept it during the dream; only after waking up are you able to rationalize that the content of the dream was impossible.)

If the second half is not a dream, then civilization is collapsing off-screen
The entirety of the film takes place at a remote, wealthy estate. We never hear or see any news reports about what is almost certainly the single biggest event in recorded human history. Given what that event is, the rest of the world must be in utter chaos.

The planet is simply a metaphor for the ways in which depression destroys lives on both the individual and family level.
Justine's wedding shows a more prosaic sense of how depression can wrack an entire family, but the second half of the film is more an abstract reflection on the aftermath of how depression ravages a family. When Claire does a search for "melancholia," most of the hits are simply for depression. In a way, all of the characters are simply caricatures of different styles of melancholy: Justine is depressed, inward-turned, and lethargic, while her sister Claire is more anxious and frenetic when under crisis.

This reading of Claire also explains her husband John's behavior: he tends to be dismissive of Justine's depression, of Claire's fears. He insists that Claire not surf the internet -- much like a beleaguered spouse might insist that their hypochondriac partner not surf the web -- in a manner both nurturing and condescending. However, when he realizes that the crisis is inevitable, his rational framework falls apart, and he commits suicide.