Question Help with quaternions: pose Parent->Child hierarchy to a 'transform pose' based on child offset

Setup:
Red Sphere is a child of Cyan Box

Goal:
Move / Rotate Cyan box such that Red sphere matches position / rotation of yellow sphere.

Here is what I have so far. The Update function works since the rotation is calculated before the position is set.
However, the fixed update function is not working. I believe this is due to the transforms being updated only after both the position and rotation is set.

How can I fix this? Any help is appreciated!

Thanks!

Code (CSharp):

1. private void FixedUpdate() {
2.     Quaternion localRotation = Quaternion.Inverse(red.rotation) * cyan.rotation;
3.     cyan.Rigidbody.rotation = (yellow.rotation * localRotation);
4.     cyan.Rigidbody.position = (cyan.position + (yellow.position - red.position));
5. }
6. private void Update() {
7.     Quaternion localRotation = Quaternion.Inverse(red.rotation) * cyan.rotation;
8.     cyan.transform.rotation = (yellow.rotation * localRotation);
9.     cyan.transform.position = (cyan.position + (yellow.position - red.position));
10. }