Taxonomies are not child of each other unlike terms, which can be. Take a look at this flowchart:
Model is a child of Make, and should not be registered as a new taxonomy. What you are trying to do, is something like setting Ford as a child of Honda, which is not right. Instead, register 1 single Make taxonomy, and then create sub-taxonomies, just like what we do in categories.
Take a look at register_taxonomy() function at the codex, and register your taxonomy as hierarchical, then create sub taxonomies as model.