Akinbo,
I don't 'have a difficulty', it's just a flawed conception. I suspect being unfamiliar with astronomy you've long harboured a false conception of bunches of 'objects', (i.e. components of a galaxy), moving THROUGH 'space'.
That's incorrect. The local 'space' moves WITH the 'inertial systems'. Even the editor of Sci Am recently wrote about how galaxies rotate in what he termed 'lockstep', i.e. whole galaxies rotate like 'dinner plates', complete with the interstellar medium, (and halo and satellites out to many k light years) in the same way that it's not Earth' that orbits the sun but the whole Earth 'system'; atmoshpere, ionosphere, magnetosphere, plasmasphere.. EVERYTHING, at rest with the centre of mass of the central dense 'body'. Light does 'c' within that zone WRT THE LOCAL centre of mass frame, just like it does c through the ISM wrt the local Centre of mass GALAXY rest frame.
That's the dichotomy, never resolved relativistically, of the "ecliptic plane issue" identified in my 2012 essay, IAU 2000 and for instance USNO Circ 179. (p6). The sun's kinetic 'domain limit' is the heliosheath, which is why Voyager appears to have 'slowed down' from our frame after crossing it. 100 years ago they thought space was 'nothing'. No wonder the residual confusion! But the POSTULATES of SR make perfect sense; inertial systems are 'nested'.
In simplistic terms, space IS a 'medium' (which is why it can expand!) and indeed contains far more of the mass/energy of the universe than baryonic matter! (objects') approx 70% as opposed to just 4%! Once you've grasped that conception you'll far better understand the video and concept of 'bulk flows' of the regions. EACH has it's own local CMB rest frame.
You'll find a whole host of anomalies can be resolved once the confused 'interpretations' of SR are removed to allow causal logic to return!
best wishes
Peter