There is no such thing as "outside our universe". Anything which has the ability to be "outside" would, by definition, be inside the universe.
If we are one of multiple universes, they cannot interact through the eleven dimensions of string theory (whichever of those might exist. What I mean is: none of the physical dimensions we know about) - they cannot pull on objects within our universe. If they could, we should be able to see them (electromagnetism and gravity move at equal speeds. If something attracts you, you must be able to see it (We can only see within our universe (we can see the edge of what we can see, and it is within our universe), so we know that gravity is not the cause of our expansion))
"Dark Energy" is merely a placeholder. We don't know what it really is, we just know that the universe acts like there is an extremely small unbound energy for every unit volume of space, which cannot be explained by the effect of quantum energy (it is, due to quantum mechanics, impossible to have something be completely without energy) or cosmic background radiation, or any form of currently known force whatsoever.
What you are doing is assuming more, not less, than those who simply say "dark energy". They know it's not an explanation, it merely describes what it acts like, while leaving it open for better interpretation. What you are doing is wrongly assuming dark energy is a final answer, and then making your own, even more complicated, solution of your own.
To expand on what nyph says: general relativity - the current model of gravitation - allows for a so-called "universal constant" to exist within it, which acts exactly like dark energy: as if there is an energy pushing everything apart in every volume of space. However, the cause of that "universal constant" is completely unknown too. What this means is that gravity does not disallow dark energy - there is no contradiction between dark energy and gravity in the same way there is a contradiction between gravity and the standard model.