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 Quote by olivermsun The residual vectors really are equal, meaning pointing the same direction, once the earth rotation at 1/lunar orbit is taken out.
I have not idea what you mean by "residual vectors" and "taking out the earth rotation". The inertial centrifugal force in rotating frames points away from the frame's axis of rotation, and has the magnitude m $\omega$2 r, where $\omega$ is the angular velocity of the frame, and r is the distance to the frame's axis of rotation. So again:

In which rotating frame would the centrifugal force vector be the same for A & B (as shown in the picture)?

 Quote by olivermsun It provides the constant offset which allows the tide-producing force to be pointing toward the moon on the near side and away on the far side while
A uniform inertial force field causes uniform acceleration, so it cannot cause or contribute to any deformation (tides).