How to list custom taxonomy 1 terms related to current taxonomy 2 term

Hey,

I have a custom post type “Products” that have two Taxonomy: “Categories” and “Counties”.
My problem is:
When I visit a Categories Term page that have children, I want to list name of all Counties terms related to current Categories term and his children.

I have this code that list me all Counties terms related only to current term, not and his children.

$taxomnomy = get_queried_object();
        $cat = $taxomnomy->term_taxonomy_id; // current categories term id
        $taxonomy = 'counties';
        $sql = "
        SELECT DISTINCT t2.name
        FROM $wpdb->terms t2
        JOIN $wpdb->term_taxonomy tt2 ON (t2.term_id = tt2.term_id
              AND tt2.taxonomy = '$taxonomy')
        JOIN $wpdb->term_relationships tr2 ON (tt2.term_taxonomy_id = tr2.term_taxonomy_id)
        JOIN $wpdb->posts p ON tr2.object_id = p.ID
        JOIN $wpdb->term_relationships tr ON  (p.ID = tr.object_id
                 AND tr.term_taxonomy_id = $cat)
        ORDER BY t2.name ASC
        ";
        // print_r("<p>SQL:$sql</p>");
        $values = $wpdb->get_col($sql);
        // print_r($values);
        foreach ( $values as $term ) {
        echo 'County: '.$term;
        }

Thanks.