As I wrote in my previous message, I came up with a solution, and by reading you, it seems this is what you want. Please, find below the code I use to display sub-categories. It will display them in both Category pages, and in the post where it belongs. However, you have to give the category parent ID where the sub-categories belong in order to display them:
<?php /* Display sub-categories, you have to add manually the parent catgeory ID concerned */ $this_category = get_category($cat); if (($this_category->cat_ID == 1) or ($this_category->cat_ID == 4) or ($this_category->cat_ID == 5)) { ?>
<h4><?php echo $this_category->cat_name; ?>Sub-Categories:</h4>
<ul class="sub-categories">
<?php wp_list_cats('sort_column=ID&sort_order=asc&list=1&optioncount=0&hide_empty=0&use_desc_for_title=1&children=0&child_of='.$cat.'&Categories=0&hierarchical=1'); ?>
</ul>
<?php } elseif (($this_category->category_parent == 1) or ($this_category->category_parent == 4) or ($this_category->category_parent == 5)) { ?>
<h4><?php echo(get_category_parents($this_category->category_parent, FALSE, '', FALSE)); ?>Sub-Categories:</h4>
<ul class="sub-categories">
<?php wp_list_cats('sort_column=ID&sort_order=asc&list=1&optioncount=0&hide_empty=0&use_desc_for_title=1&children=0&child_of='.$this_category->category_parent.'&Categories=0&hierarchical=1'); ?>
</ul>
<?php } /* end of Display sub-categories */ ?>
Note: it must be inside The Loop. It put this in my sidebar, so, your sidebar must be within The Loop.