Have Star Trek Federation space stations ever performed major maneuvers? These could be for example a 180 rotation about an axis, move to a new location, avoid a collision, enter into an orbit, etc. (All Star Treks)
In the pilot episode of Star Trek: Deep Space Nine, they use the station's thrusters and deflector field to move DS9 from orbit around Bajor XI (AKA "Bajor", the one that the Bajorans come from) to the mouth of the Bajoran wormhole. The wormhole is located in the Denorios belt between Bajor IX and Bajor X. Based on the distances between planets in our own solar system, this relocation was somewhere between 108 and 109 miles.
Here is a map of the Bajoran system that someone might be able to use to glean more information about the distance involved. The numbers above the planets don't seem to refer to distance:
Edit: according to Star Trek Star Charts, the Bajoran sun is a G2V class star with an absolute magnitude of 4.7, very similar to our own sun (G2V 4.83). So assuming Bajor XI is about the same distance from its sun as Earth is from ours (9.3*107 miles), and assuming the distances shown in the map are to scale (which I doubt, for the record), then the distance between Bajor XI and Deep Space Nine's location is approximately 3.5*107 miles, much shorter than I expected, and about 2/3 of the distance to Mars's closest approach to the Earth.
Also, Deep Space Nine rotates constantly, but AFAIK its a continuous , unpowered rotation that doesn't count as a "maneuver" in my opinion.
Technically Deep Space Nine was built by the Cardassians, owned by the Bajorans, and administrated by the Federation, so I'm not 100% certain whether it qualifies as a "Federation space station", but presumably it would become one once Bajor eventually joined the Federation (which never officially happened in canon to my knowledge but was always the writers' eventual intent).