I must be missing something basic here.
The short version:
I want child objects to rotate around the parent’s axes, not their own local axes.
The long version:
I have two cubes: one at world origin, the other at 0,0,1. The one at 0,0,1 is the child of the cube at origin. When I rotate the origin cube the other cube inherits the rotation, but not the relative position. ie. it rotates around its own axes, not the parent’s axes.