Suppose two bodies S and L are in proximity (asteroids say). L is substantially larger than S. For simplicity, let them initially have negligible angular and linear velocity.
S will begin to fall towards L. Since S is in free fall it feels no inertial effects.
Now, S is instrumented with a laser range finder which may be used to measure it's acceleration a. When a reaches some set value thrusters on L activate causing it to accelerate away from S also at a.
Prima facie, it would appear that we have a stable system wherein S is accelerated at a but feels no inertial effects. This seems problematic (e.g. the distinction in the twins paradox is said to be that the moving twin feels accelerated).
Where is the flaw? Perhaps S feels inertial forces on account of some kind of tidal effects?