Get direct children of custom taxonomy

I've googled extensively and tried my best, but I just can't get the first level children of the custom taxonomy in the code below to work! It only displays the parent level. What I am trying to achieve is the following:

Level 1  <--- at the moment, it only displays this level
  Level 2  <-- I want to display this level too
    Level 3  <-- but NOT this level

This is my code so far:

    // get children of current parent.
    // $tchildren = get_term_children($term->term_id, $taxonomy); //returns all children
    $uchildren =get_terms( $taxonomy, array('hide_empty' => 0 , 'parent' => 1));

    $children = array();
    foreach ($uchildren as $child) {
        $cterm = get_term_by( 'id', $child, $taxonomy );
        // If include array set, exclude unless in array.
        if ( is_array( $include ) && ! in_array( $cterm->slug, $include ) ) continue;
        $children[$cterm->name] = $cterm;
    }
    ksort($children);

    // OPTGROUP FOR PARENTS
    if (count($children) > 0 ) {
         if ($term->count > 0)
             $list_of_terms .= '<option class ="group-result" value="'.$term->slug.'" '.$select.'>' . $term->name .' </option>';
    } else
        $list_of_terms .= '<option value="'.$term->slug.'" '.$select.'>'. $term->name .' </option>';

    // now the CHILDREN.
    foreach($children as $child) {
         $select = ($current_selected == $child->slug) ? "selected" : ""; // Note: child, not cterm
         $list_of_terms .= '<option class="result-sub" value="'.$child->slug.'" '.$select.'>'. $child->name.' </option>';

    } //end foreach

If someone can help me with this beast, you'll be my freaken hero!