Layer needs to be fixed/unmovable within puppet

Hi everyone, 

I'm animating puppets being in a car right now,

but the problem is that the seat and belt move with the puppets breathing/slight body movements. I can also add the seats afterwards in AE, but since the seatbelt is going under one arm and over the other, I need it to be within the puppet but not move at all. Is there any way I can do that?

Thanks for any help! 🙂

"Gurt" is the seatbelt and "Sitz" the seat. I've made them independent and pinned them, but that doesn't make a difference regarding the movement.