First off, the cube has a rotation of 90,0,90
This type of thing is generally easier when all rotations are cleared out when an assembly is in its default pose.
That said, as long as the cube only needs to rotate in one axis (like a door opening) you can just include “Rot Z” in the ChildOf constraint of the latch bar object. (when you first make that change, the latch bar will rotate and you’ll have to counter rotate it, but then it should behave properly)
If the cube need to rotate in multiple directions, I would suggest using actual child-parent relationships rather than constraints. Then you’ll have to manually rotate the latch bar, or set up ipo drivers:
BTW, I don’t think the latch manipulation object is necessary for what you’re trying to do. If it’s just visual, you can join it with the latch lever.