re: Barycenter Inside Planet Versus Outside
The key distinction is that in the case of a satellite the center of the orbit lies inside the *other* body. For the parent body, the center is within itself. In effect the satellite is just causing a wobble on the parent body.
The same fact holds in regards to the planets and the Sun.
Just calling the larger the parent body would cause problems when the two bodies had close to the same mass.
Bob Clark