Sorry not to be able to replicate. I just tried this with 2014.0, works as expected with one shape and one text layer.
Don't you have three layers: text, large diamond and small diamond?
Everything has the same z-axis value, right?
Yes, it's two shape layers and one text layer. It only happens with the solid diamond (which is parented to the hollow diamond). Not sure how the parenting is making the text (which is unparented) behave like that.
All layers 2D.
Here's the project: http://www.mediafire.com/download/vtt5ub939bcjadh/WeirdShapeMovementCS6.aep
I can replicate your behavior by selecting the text layer and the diamond layer then dragging. That's completely normal because the position parented diamond layer becomes 0,0 when parented and movement of the selected Text layer is based on the recalculated positions. When you get all layers to move together you have selected all 3 ayers. The behavior is completely normal. The only way to prevent this kind of odd movement when selecting two objects, one of which is parented to another, is to work in a square composition. If you can wrap your head around the math you'll figure out why.