a)
I don't see where "child" is initialized.
You're initializing the position once when the RigidBodyInstance is created. At that time it is not sure (but unlikely) that the child node already exists.
You should query the childs position in the _fixed_process right before you set it.
Aside from that I don't see the sense in it. If you set the parents position then this will usually move the child as well resulting in a kind of feedback loop.