Two items under one peg move at different rates

I have this weird problem: I’ve got two groups of items linked together under one peg (one an image of a head and the other a collection of drawings making a stick figure), and when I try to move the main linking peg somewhere, the two items move a different rates. The stick figure moves as I move the mouse, but the head part moves faster to whatever direction I move, disconnecting from the other image it’s connected to in the process and gaining some distance from it, so the object breaks into two. It’s still together, just dislocated from it. Any ideas what I’m doing wrong that this happens?

This could be a perspective effect, if the items are too close to the camera.
Does it happen if you move them further back in the Z-axis and scale the
peg to compensate for the size?

If that doesn’t work, are there any rotations involved?

Yep, that was it. I used pretty wild numbers for the Z access, and that’s what caused the erratic movements. Thanks!