The correct answer is:
$Pages = wp_list_pages('child_of=".($post->post_parent != false ? $post->post_parent : $post->ID)."&title_li=&echo=0&depth=1');
$InnerPages = wp_list_pages('child_of=".($post->post_child != false ? $post->post_child : $post->ID)."&title_li=&echo=0');
$Title = ($post->post_child != false) ? trim(get_the_title($post->post_child)) : trim(wp_title('', false));
if($Title != '')
$Pages = str_replace($Title.'</a></li>',
$Title.'</a>'.
'<ul id="test"><li>Overview</li>'.$InnerPages.'</ul></li>',
$Pages);
echo $Pages;
unset($Pages, $InnerPages);
HOWEVER, I have found a much better solution to accomplish what I was trying to do: How to add active class to custom menu using while loop and wp_list_pages