[dahart]

Which law are you thinking of? There isn't a physical law I'm aware of that claims gravitational attraction toward a center of mass, you might be conflating several laws or thinking of an approximation rule that was never intended to cover one object inside or even near another.

Newton's law of gravitation is stated in terms of a particle to particle relationship.

Center of Mass is the balance point of an object, and objects will always rotate around their center of mass unless constrained, but this doesn't relate to gravity.

You can approximate gravity at a distance from any object by using the object's center of mass, but that approximation breaks down when you're close to it.