A question from 3 years ago got an answer that would be a great answer to a different question (and concluded with a comment that more would be posted later.) Let me re-ask, making the question clearer.
Normally, ISS spins at 1 revolution per orbit, effectively one side always facing the Earth.
With two bodies in almost the same orbit, they move in an elliptical trajectory respective to each other (for example, the loose antenna cover seems to orbit ISS, even if it's not gravitationally bound to it).
The docking maneuver takes good several minutes, which comprise a good part of an orbit. If I brought Soyuz to a dead stop relative to the station 200m below the bottom port while ISS is facing Earth with it, the orbital mechanics would move me to 200m above the station within 45 minutes (half the orbital period) - or move me 45 degrees off course within some 11 minutes.
How is this dealt with? Is ISS rotation relative to Earth stopped (ISS attitude becoming constant relative to distant stars, changing relative to Earth) or does the docking ship deal with it using RCS to account for the drift? Or is this even different or I made some wrong assumptions?