face does not stick to the head

I got the link to the project you uploaded. A few suggestions, but you need to try them to see if they are what you want to happen.

• I suggest removing the independence from the "face background" layer. Either unclick the crow for that layer, or remove the leading "+" in the layer name in Illustrator (that leading "+" makes CH add the independence flag for you automatically)
• I suggest adding the independence flag to the "Head" layer (rename it to "+Head"). That way the head will rotate, but once the above step is done it will attach to the body.
• Change the "Head Position Strength" property of the "Face" behavior from 100% to 0% - it is making the head fly away from the main body too much.
  

   

• For this puppet, I think you don't want the mouth independent - I think you want to remove the leading "+" from Mouth and Sad Mouth, so the artwork stays lined up better.
• In your Left Eye you have a "Right Blink" layer - rename it to "Left Blink".
• I am not sure if you want your eyes to move, but there is not enough there at present to make them move. You normally have an area for themto move in - you simply might not need it for this puppet, which is fine.
• I don't think you have triggers set up for the sad mouth yet - but maybe you don't need it? If not, just delete the sadmouth layer. If you want to keep it, I recommend renaming to "Sad Mouth" with a space. I also recommend putting Mouth and Sad Mouth under a layer like "Mouths". I like grouping swap set members under the same group - makes it easier to understand. (But I suspect, at least for now, you can just delete the Sadmouth layer).

It was working a fair bit better after doing the above.

I still think you probably do not want face background independent, but the reason given was not quite right.

First, a quick primer on meshes and independence.  CH has a tree of layers, and a tree of meshes. A new mesh is started when you mark a node as independent. The mesh controls how the artwork is warped and twisted etc, so all the artwork on the same mesh move together.

You start making eyes independent as you like them to move without the rest of the face artwork moving. Same is usually true of the mouth, eyebrows, etc. So you normally make parts of the face independent.

If you want the head to swivel separate to the body, you normally make the Head layer independent. But a layer must have some artwork in it for children to attach to it. So as soon as you make Head independent in your case (if you want it to swivel without moving the body) you probably want the face background NOT independent - it is the primary artwork for the head mesh.

Child meshes (child layers that are marked independent) attach to parent meshes  by having the origin set to a position over the artwork of the parent. So if you have the full face artwork not independent, normally all the face features are over the top so attach easily without you having to do anything. But if your head artwork is independent, the eyes etc might have trouble attaching to the parent.

So, I still think you want your face artwork NOT independent. You *might* want you head independent (up to you). But the reason I gave before was not 100% correct.

When you mark something as independent, it will float free unless you attach it to artwork in the parent mesh. Your Head layer has no artwork in it - all children are marked as independent, so there is nothing to attach to, so everything there is effectively disconnected. Try making face-background not independent. That should then include that artwork in the Head mesh, giving the mouth and eyes somet4hing to attach to