The head, which is a face background, just keeps squashing and stretching like a waterbed when I move my head. And the pupil just seems to drift around. How to I fix it?
I had this happen too-
Check your tags. If ithe squash and stretch are happening with your eyebrows, theres an eye brow tag in there somewhere. CH tries to auto-tag things and sometimes doesnt get it quite right.
What can happen is some part of the puppet gets "stuck" (pinned in effect) by a behavior (like the Face behavior). Eyes are a common cause of problems. The quickest little tool to help is the "mesh" icon at the bottom of the scene window which shows a mesh of little yellow triangles across the puppet. When it starts moving, you can often see what part of the puppet is not moving which helps track down what area of the puppet is wrong.
If its the eyebrows, then you have to decide whether you want the eyebrows (and other eye parts) to be "independent" so they move without distorting the rest of the face. If you want it to distort the face a bit, then you might want sticks or pins to restrict how much such movements affect the rest of the head. So I think its both tags and independence you need to think about. Another mistake is to go tooo crazy with independence layers.
I had so many problems and questions about eyes, I wrote up a blog saying how I debug the most common problems. https://extra-ordinary.tv/2018/04/21/debugging-character-animator-eyess/
One other reason for this is that if you don't have blink tags and your eyes are not warp independent the face behavior will attempt to apply vertical scaling to the eyes to "blink" them with simple scaling, which can make the head warp strangely.
I think in 2.0 this behavior has been restricted so it only happens when the eyes are warp independent, so that may fix it, too.