If the main engine is gimballed, gimballing the chairs may make sense. But using RCS seems far simpler, and has been demonstrated in-episode.
During gravitational slingshots, the accelerations of crew and spacecraft should be exactly identical because they are both in the same gravitational field, which acts on all mass identically (i.e. the crew should experience freefall until they burn).
Yes, you can do really cool stuff with atmospheres. Aerogravity assists (using an atmosphere to generate lift and do a 180 around a planet to put you into a retrograde orbit, check it out
) are really, really, awesome, and the sort of thing you might want to do. This is the only situation I can imagine that would exert centripetal forces on spacecraft (actually, it's acting as an aircraft now) but not crew.
Yes, you might need a reclining chair for that. But probably not gimbals, although they might look cooler.
For simple aerobraking/capture, the deceleration should be towards the rear of the spacecraft (assuming the pointy end goes into the atmosphere while the big engine bell is protected by the pointy end). Same couches are good.
For leisurely, <1g burns, a sitting chair is better than a reclined chair for comfort; but at >1g, a reclined chair improves crew survival. Hence the reclining. That might justify a chair capable of 180 rotation (and explains the recliners).