php IF function question

I have a bit of php listing a submenu if the current category has children. However, it does not list this submenu if a submenu item is clicked.

This is what I’ve got:

<ul id="menu" class="clearfloat">
	<li><a href="<?php echo get_option('home'); ?>/" class="on">Home</a></li>
 	<?php wp_list_categories('orderby=name&exlude=181&title_li=');
 	$this_category = get_category($cat);
 	if (get_category_children($this_category->cat_ID) != "") {
 		echo "<ul>";
 		echo "</ul>";
 	}
	?>
</ul>

<ul id="submenu">
 	<?php if (get_category_children($this_category->cat_ID) != "") { ;?>
	<?php wp_list_categories('orderby=id&show_count=0&title_li=&use_desc_for_title=1&child_of='.$this_category->cat_ID); };?>
</ul>

So when a main category item is clicked, I’m taken to that category and all of its children are listed. However, if I click on a child category, once I arrive there are no children listed… obviously, since I don’t have children of children categories.

So how could I modify this IF statement at the end to also show me the children categories if indeed I’m at a page that is a child category?