When you add an object to a parent as a child and then change the parent's rotation or position, it will only affect the parent.
The child element's values remain untouched, but its position and rotation are calculated relative to the parent. There is no stored relationship between the child and the parent of the parent, which is why you cannot save the child's rotation in relation to the parent of the parent.
If you want to move along with the parent element only, you can calculate the children's position or rotation relative to the parent of the parent and store this information somewhere. However, setting this position and rotation for each child in every animation frame may not be practical.
To determine the child's position relative to the parent scene, refer to this guide on how to get the global/world position of a child object
A more effective approach
is to place other elements into the scene separately, rather than as child objects. If you need to perform operations on a group of objects, save their identifiers externally and retrieve the object by identifier when needed.
scene.getObjectById( 4, true );