Wordpress - Change order of Custom Taxonomy List

After quite a bit of searching and extensive tests, I found the answer.

Add this code to your theme's functions.php:

function set_the_terms_in_order ( $terms, $id, $taxonomy ) {
    $terms = wp_cache_get( $id, "{$taxonomy}_relationships_sorted" );
    if ( false === $terms ) {
        $terms = wp_get_object_terms( $id, $taxonomy, array( 'orderby' => 'term_order' ) );
        wp_cache_add($id, $terms, $taxonomy . '_relationships_sorted');
    }
    return $terms;
}
add_filter( 'get_the_terms', 'set_the_terms_in_order' , 10, 4 );

function do_the_terms_in_order () {
    global $wp_taxonomies;  //fixed missing semicolon
    // the following relates to tags, but you can add more lines like this for any taxonomy
    $wp_taxonomies['post_tag']->sort = true;
    $wp_taxonomies['post_tag']->args = array( 'orderby' => 'term_order' );    
}
add_action( 'init', 'do_the_terms_in_order');

(Credit: this is based on - but improved - http://wordpress.kdari.net/2011/07/listing-tags-in-custom-order.html)

I've been struggling to find the answer to alphabetical child terms of a custom taxonomy ... I wouldn't recommend altering core WP files, so here's what I added to my taxonomy.php file to list out custom taxonomy descriptions, with links to child terms in alphabetical order. Modify to suit your needs, I hope this helps someone out there.

// Get Main Taxonomy for use in template file
$term = get_term_by( 'slug', get_query_var( 'term' ), get_query_var( 'taxonomy' ) );
$termTaxonomy = $term->taxonomy;

<h1><?php echo apply_filters( 'the_title', $term->name ); ?></h1>

<?php // test for description before unleashing a div 
if ( !empty( $term->description ) ): 
  echo '<div class="description">';
  echo $term->description;
  echo '</div>;
endif; ?>

// Now get children terms, using get_term & 'child_of' get's us alphabetical order
$termchildren = get_terms( $termTaxonomy, array(
  'child_of'     => $term->term_id,
  'hierarchical' => 0,
  'fields'       => 'ids',
  'hide_empty'   => 0
) );

// Make an alphabetical linked list
echo '<ul>';
foreach ($termchildren as $child) {
  $term = get_term_by( 'id', $child, $termTaxonomy );

  // Modify this echo to customize the output for each child term
  echo '<li><a href="' . get_term_link( $term->name, $termTaxonomy ) . '" alt="' .$term->description. '">' . $term->name . '</a></li>';
}
echo '</ul>';

I know this is kind of cheating, but you could always use the Simple Custom Post Order plugin. It's free, and it allows you to sort Taxonomies in addition to Post Types.