I don’t have any experience with the SDK, but based on my experience with the SketchUp DOM from using the Ruby API, the parent of a component instance is a component definition, not the containing component instance.
This means one single component instance can be placed on multiple different places in the model, if any of its parent components has more than one instance. To specify the location of a component instance in model space you must specify the path of instances leading down the hierarchy to it. Only in the trivial case of exactly one instance of each parent definition, you can know the position in model space only from an instance.’
Typically when exporting geometry (to formats that don’t have SketchUp’s definition/instance model) you traverse the document hierarchy from root to leaf, thus always having a reference to the parent instances, and their transformations.
This example shows how you can traverse or “drill into” a model recursively, while maintaining a reference to the local transformation. It’s written in Ruby but maybe can be helpful anyway to understand the “model model”. https://github.com/Eneroth3/Eneroth-Face-Area-Counter/blob/master/src/ene_material_area/main.rb
