How to exclude parent category but show child categories?

I spent almost two months building and debugging Total Widget Control to do exactly this for all of a sites widgets. Bear with me as I strip the code out of Total Widget Control and try to make it usable for you.

    global $wp_query
    $twc_menu_item_object = $wp_query->object_id; //is the object id of the current page.
    $objects['menu-item-object'] = ''; //the object id of the tax to display under

    if ( taxonomy_exists($twc_menu_item_object) && isset($objects['menu-item-object']) )
    {
        foreach ($objects['menu-item-object'] as $menu_id => $menu_type)
        {
            if ( $menu_type != $twc_menu_item_object ) continue;
            if ( !cat_is_ancestor_of( $menu_id, $object_id ) ) continue;
            return true;
        }
    }
     return false;