I think you might be referring to the very recent and tentative discovery of a "dark flow", where, as well as the overall expansion, there may also be some peculiar motion towards a specific part of the sky. The findings are unconfirmed so far, but have no great impact in the overall picture of expansion, as far as I can tell.

If there is a "dark flow", some speculative theories do indeed attribute it to a concentration of mass outside of our currently observable part of the universe, but within our particle horizon (our past light-cone).

But an unseen mass cannot be responsible for the overall expansion of the universe. The main problems you are having interpreting the diagrams presented to you is the failure to differentiate between a global and a local picture of what is going on.

I steer clear of diagrams myself, and use a conceptual 3D grid of coordinates instead to show the global picture, and then we do some maths within that grid to show the local picture.

So, imagine a 3D grid, and put an observer at every intersection point in that grid. Let's say we make each intersection point 1 meter apart, so wherever there is an observer, if they look along any axis, they see points 1, 2, 3, 4, 5 etc meters away, receding into the distance as far as they can see.

Now we expand that whole grid to 10 times its original size, in 1 second (these figures make the maths easy). The whole grid expands at the same rate throughout, and after the expansion each intersection point is now 10 meters from its nearest neighbour along any axis.

The global view is that the whole thing expanded equally throughout, so hopefully you can see that no gravity from "outside" the grid could cause this kind of expansion.

But what of the view of an local observer? Well, in the space of 1 second, their nearest neighbouring point receded from 1 to 10 meters away, meaning it receded at 9 meters per second. The next point along receded from 2 to 20 meters away, meaning it receded at 18 meters per second. The fifth point moved from 5 to 50 meters away, receding at 45 meters per second! The further away a point is from an observer, the faster it recedes!

(A point 33,000,000 meters away will have receded to 330,000,000 meters away in one second, meaning it has receded at the speed of light)

And the view of an observer would be the same, wherever the observer was within that grid. In the context of a "dark flow", perhaps all the observers have been pulled a little bit off of their intersection points by a flow in a certain direction within the grid, but the grid still expands in the same way.

The problems we have in observing the overall picture are two-fold. We are limited to the speed of the light that we use to build up the picture, and the canvas has expanded at different rates throughout history. But the rate of expansion is a global effect, so those gaps between conceptual intersection points are always equal. As the rate of expansion changes, it changes throughout. But it affects our local picture, so we see the grid with different sized gaps, as we look back across time.