Multiple Loops That Pull Pages (Child/Grandchild) While Styling the First Entry

You have so many things wrong with your code, to start WP_Query does not have 'sort_column' , or 'depth' parameters. the use of $do_not_duplicate = $post->ID; does nothing at all and a few other things.

What you need is to get the children (just the ids, no need to get the post object since you are not using any of the fields other then title and premalink), loop over them and for each one get the children (meaning main page grandchildren) and loop over them.

something like this:

<?php   
//store page
$temp = $post;
//get children
$children = get_posts(array(
    'orderby'  => 'menu_order',
    'post_per_page' => 30, 
    'post_parent' => $post->ID, 
    'post_type' => 'page',
    'fields' => 'ids')
);
//children loop
foreach ($children as $child) {
    $do_not_duplicate[] = $child;
    ?>
    <div id="child">
        <h2 class="clear"><a href="https://wordpress.stackexchange.com/questions/43191/<?php echo get_permalink($child); ?>" ><?php echo get_the_title($child); ?></a></h2>
    </div> <?php
    //get grandchildren
    $grandchildren = get_posts(array(
        'orderby'  => 'menu_order',
        'post_per_page' => 3, 
        'post_parent' => $child, 
        'post_type' => 'page',
        'fields' => 'ids')
    );
    $count = 0;
    //grandchildren loop
    foreach($grandchildren as $granchild){
        setup_postdata($granchild);
        $count++;
        if ($count == 0){ ?>
            <div id="top">
                <div class="first">&nbsp;</div>
                <h3 class="clear"><a href="<?php the_permalink($granchild); ?>" ><?php the_title($granchild); ?></a></h3>
                <?php echo get_the_post_thumbnail($granchild->ID, 'thumbnail'); ?>
                <p class="clear"><?php the_content('read more...'); ?></p>
            </div> <?php 
        }elseif ($count == 1){ ?>  
            <div class="middle">
                <h3><a href="https://wordpress.stackexchange.com/questions/43191/<?php the_permalink(); ?>" ><?php the_title(); ?></a></h3>
                <p class="clear"><?php the_content('read more...'); ?></p>
            </div> <?php
        }else { ?>  
            <div class="last">
                <h3><a href="https://wordpress.stackexchange.com/questions/43191/<?php the_permalink(); ?>" ><?php the_title(); ?></a></h3>
                <p class="clear"><?php the_content('read more...'); ?></p>
            </div><?php
        }
    }
}
//restore page
$post = $temp;