I have a collision box set up parented to an armature and a mesh with dynamic physics. When I use simple motion rotation logic block, the armature becomes uncentered with my collision box. I checked that all my origins were centered and observed the rotation from my workspace and everything seems to be working there as it should.
I have the file here if it helps to understand my problem
You seem to have un-uniform scales between parented objects. This often leads to funky relationships between their movements.
Select each one and Apply Scale (ctrl+A, select Scale), and you’re good to go!