There is some features in AE (never tried it, not sure what it is called, but has been discussed in forums before). You can use AE to track a marker object and associate the imported CH content with that tracking. This is nothing to do with CH - you can use it to make an object (or video clip) track the marker.
But sorry, not sure what it is called in AE and not sure if it will do rotation etc as well or just X/Y positioning. People had discussed putting a green dot on their forehead for example so the puppet superimposes over the top.
Object tracking... Hmm.
Seems a bit "hacky" for something which should be pretty simple to implement. It would probably work though.
You can certainly do keyframing (better than what is in CH) to move the video/puppet about in AE. I may have misunderstood - I thought you wanted the puppet to track a real world head! 😉
But it might be a better question on how to attach sub-objects to parent objects in the AE forum. For example, if you export a video (instead of using dynamic linking) then its just AE managing overlapping videos. If you can get that going, I bet the same approach works for dynamic linked CH objects as well.