Does the category module have a setting that shows the sub-categories when viewing the parent one? I see this is possible on the StackIdeas forum (when I click the "EasySocial" category it then displays its sub-categories).
Attached is a screenshot showing a parent category landing page that has sub-categories, but I manually need to click the down arrow in the module to view the sub-category list. I've also included the module's settings.