So this question is fairly hard to word but I hope it attracts the attention of the knowledgeable...
I have a model of a person, a viking to be specific. This viking has a mustache and a rig. His mustache pivots along the head bone as intended but it rotates on the wrong point so it doesn't exactly stay attached to his head. It's a little complicated since the Mustache is a separate model but joined with this one. It uses separate vertices and stuff if that's relevant. The mustache has full weight influence but it doesn't help since the problem is with the pivot point it's following.
Here's a vid to explain it -