You confuse dark matter and dark energy. The later is the name for the energy that accelerates the expansion of the universe.
The rest of your hypothesis also has no sense, given what we know today. The big "black hole" can't be "outside" of our universe as our universe is all that is, including the space in which it is.
The universe doesn't expand inside of its own space, there is actually more space between the galaxies appearing, that is, the new space is appearing, according to what we observe. So the mechanism can't be easily explained by imagining some mass "outside" as the mass must be in the very space we talk about.
What we see we call the "observable universe" and because of the finite speed of light, observing the stuff in the distance we see the past! What we see in the farthest distance is actually just a glow of the so-called "big bang," a phase of the universe when there were no stars, no galaxies, just the elementary particles, specifically, we see the moment in which that state became "visible", that is, allowed the photons to travel long enough.
So the farthest everywhere we look is just the glow. It is all around because around the point where we are now, just like any other point, there was much less space early enough. The glow is called the CMB:
https://en.wikipedia.org/wiki/Cosmic_microwave_background
It was first time measured in 1964, and the scientists received 1978 Nobel Prize in Physics for that.
We see the big bang in the distance, even if the big bang ended around 14 billion years ago.
I hope you see why we can't explain what we actually observe by imagining the "black hole outside."