The ISS does do maneuvers, usually to avoid incoming orbital debris, which as you can guess at those speeds are quite deadly. This maneuver is called a DAM (Debris Avoidance Maneuver) and is usually performed often 30 hours or more before TCA (Time of Closest Approach) with about two hours of actual moving. Yes the ISS is in orbit, so there are different conditions, but the premise is the same. Its is a rare event however. A mothership in our sense would not need to avoid such debris obviously, since its shields can handle even large asteroids with ease (depending what they are made out of and at what velocity the object has relative to the vessel).
The key here is detection. USSTRATCOM
tracks orbital debris pretty carefully alongside other such organizations for dangerous particulates and trash here on Earth. Onboard a mothership, sensors would probably sweep the space in front of and around the ship for incoming dangers. Depending on the speed of the mothership and the sensitivity of the instruments, the ship could have days or even weeks to prepare for precautions, whether it be to veer away from the incoming object or blast it with a laser (for example) to deflect it enough for the ship to slip by or break up into smaller, more convenient pieces.
I imagine that strategically, we would send our motherships in fleets, as the old exploratory sea expeditions went, at least initially. That would mean plenty of support for the larger, less maneuverable motherships if a variety of ships serve as an entourage - as you said, with non-rotational stations, maybe housing shuttles and similar craft.
That brings us to the main point; actual moving. The fact is - motherships don't have to move around much! Their primary purpose would be to support a large population of crew (whether artificial or organic), scientific instruments, hangers for smaller craft, and a more or less a specialized HQ for a fleet. The least they would need to do is slow down, then gravity assist
into an orbit around a star or planet at their destination. Leave it to the other, smaller ships in their entourage or docked in their hangers aboard the main mothership, to move around the solar-system, or go down to the planets, mine asteroids, collect fuel etc.
Speaking of fuel, you alluded to the Tsiolkovsky rocket equation (or "Tyranny of the Rocket Equation"). I am well aware of the equation and its consequences. Inefficiency is the foe here, but there are ways to balance thrust and mass to a happy medium. We must not forget that the space craft in SE operate at interstellar distances via the Alcubierre drive (or warp drive). Lets not get into the description of this hypothetical, but scientifically feasible (maybe), technology and instead roll with it. Its methods and the nature of FTL are tricky to quantify, but at the basic level they would disregard our fears for maneuvering and slowing down, simply due to the fact that the warp bubble is not moving through space, but rather space is moving with it. As I said, lets not get into that too much (at least not now
Once at the destination, something else can be used for movement. Since in the universe of SE Alcubierre drives are possible, that means negative matter is available for use. The level of technology required to generate such matter (if it even exists) is stupendous. At these levels, an understanding of physics far surpassing our own is evident, thus the creation of ANTI-matter, via particle colliders, should be viable. Antimatter is an extremely useful (but dangerous) material, especially in propulsion. It has an efficiency of 40% relative to mass of fuel, compared to fusion propulsion (the next most efficient) that has an efficiency of only 1%. Antimatter is the most efficient fuel we can quantify with known physics, and obviously something we want for our ships. I believe the SpaceEngineer
mentioned fusion rockets being used for propulsion, but I would use antimatter instead, despite being somewhat dangerous to store.
EDIT: The 'motherships' as presented
are large for the reason that they are supposed to be, well, motherships. As in they are bigger then the ships of SE by many orders of magnitude for utility reasons.