See https://www.youtube.com/watch?v=dEaecUuEqfc or http://www.flownet.com/ron/QM.pdf for a detailed explanation.
Many worlds basically says "the wave function is real". You just take what the math says at face value, and the math says there's a blob of amplitude where the cat is alive, and another blob of amplitude where the cat is dead, and those blobs do not interact.
Copenhagen adds something on top of the math: a kind of "collapse" where the blob you did not observe gets mysteriously zeroed out. There's only one universe, which looks simpler, but the theory itself is more complex, because you just added that collapse.
Pilot Wave (of which I know nothing) seems to add a similar complexity. There's no collapse, but there's this additional non-local "wave" that's laid out on top of everything, and determines which of the blobs is real (the dead cat blob or the live cat blob).
Think Chess vs Go. Chess has rather complex rules, with an initial position, moves for 6 different pieces, and a couple special cases. Go's rules on the other hand can fit on one page. So, Go is simpler. However, in terms of possibilities, the universe generated by the Go rules is orders of magnitudes bigger than Chess'. Simpler rules can lead to more diverse possibilities. Quantum physics interpretations are similar: Many Worlds have the simplest rules, but it also describes the biggest universe.
Imagine 2 pearls on a thread. You have 2 ways to represent them: the obvious one is 2 points on a line. A less obvious (but just as valid) is a single point on a plane: the X axis would represent the first pearl, and the Y axis would represent the second pearl. Similarly, 2 billiard balls on a billiard can be represented by a single point in a 4 dimension configuration space. And the entire universe require many many more dimensions than that.
There are many more subtleties. I suggest you read the Quantum Physics Sequence for a comprehensible explanation of all this mess. http://lesswrong.com/lw/r5/the_quantum_physics_sequence/
Furthermore, I don't have a problem with accepting non-locality from a theoretical perspective either, now that I know about the Holographic Principle. If the universe is a hologram, then the apparatus that is projecting the hologram can be connected in ways that aren't obvious in the hologram.
The computer program runs inside the computer. The computer is outside the program. But nevertheless the computer's hardware is causally connected to the program. Further still, the programmer is outside the program, but he very much can influence it. Indeed, he brought it into being.
A computer program is not a universe independent of the programmer. They both exist in the same universe because they are causally connected. If they were in different universes, they must be causally disconnected. You're whole argument rests on the assumption that the program and the programmer reside in different universes, which is clearly not the case.