Puppet head need to stand not to move

I am sorry, a bit more detail could help. You mention the wall not moving but things shaking. So i will describe some principles and hopefully you can adapt it to your needs.

Lets say you want the main house outline to not change, but the 'face" on the house should move. The main way to achive this is to put the "face" in a different group and mark it independent. Any movements to the face will then not affect the rest of the house. If you want the roof of the house to be in front of the face (like hair fridge) then you might have a structure like:

+House (the root should always be independent)

- Roof (at top so in front of face)

- +Face (independent so if it moves nothing else will)

- - Eyes

- - Nose

- - Mouth (you can make independetnas well - depends of the face artwork)

- Outline (the rest of the house artwork, walls, etc you don't want to move, but is behind the face)