I attempted this...

  <?php query_posts($query_string . '&cat=9,10'); ?>

however I'd like the relaxation from the posts display underneath.

You may make something similar to this to print first one cat, then your other cat, and so the relaxation of posts. You have to make 3 querys and employ the wordpress_totally reset_query():

For instance:

<? */ loop #1 with category ID 9 */ ?>
<?php query_posts($query_string . '&cat=9'); ?>
<?php if ( have_posts() ) while ( have_posts() ) : the_post(); ?>
   <? the_title(); //just something to print out ?>
<? endwhile; wp_reset_query(); // end loop #1 and reseting query ?>

<? */ loop #2 with category ID 10 */ ?>
<?php query_posts($query_string . '&cat=10'); ?>
<?php if ( have_posts() ) while ( have_posts() ) : the_post(); ?>
    <? the_title(); //just something to print out ?>
<? endwhile; wp_reset_query(); // end loop #2 and reseting query ?>

The end result is going to be a listing of publish on cat 9, after which a listing of publish on cat 10. If you want then to print the relaxation of posts for that relaxation of groups. Do same factor again, but exclude individuals felines around the query. That´s puting a "-" around the cat parameter, like so:

<? */ loop #3 excluded categories 9 and 10 */ ?>
<?php query_posts($query_string . '&cat=-10,-9'); ?>
<?php if ( have_posts() ) while ( have_posts() ) : the_post(); ?>
    <? the_title(); //just something to print out ?>
<? endwhile; wp_reset_query(); // end loop #3 and reseting query ?>

That´s a means, might be many different ways for doing same factor, but this really is easy to understand.

Hope that can help.