Display posts from the same child taxonomy

I’m on a single post page trying to display posts from the same child taxonomy as the current post. Currently I’m getting the posts from the parent taxonomy as well, but I only want the ones from the same CHILD taxonomy.

This is what I got this far:

<?php

				//Get array of terms
				$terms = get_the_terms( $post->ID , 'destinations', 'string');
				//Pluck out the IDs to get an array of IDS
				$term_ids = wp_list_pluck($terms,'term_id');

				//Query posts with tax_query. Choose in 'IN' if want to query posts with any of the terms
				//Chose 'AND' if you want to query for posts with all terms
				  $second_query = new WP_Query( array(
				      'post_type' => 'sites',
				      'tax_query' => array(
				                    array(
				                        'taxonomy' => 'destinations' ,
				                        'field' => 'id',
				                        'terms' => $term_ids,
				                        'operator'=> 'IN' //Or 'AND' or 'NOT IN'

				                     )),
				      'posts_per_page' => 999,
				      'ignore_sticky_posts' => 1,
				      'orderby' => 'rand',
				      'post__not_in'=>array($post->ID)
				   ) );

				//Loop through posts and display...
				    if($second_query->have_posts()) { ?>

						<div class="onefourthscol"><div id="related-sites">

		<div id="related-header"><h2>Related posts
			</h2></div>

				 <?php    while ($second_query->have_posts() ) : $second_query->the_post(); ?>

				 	//MY POST CONTENT HERE//

				           <br class="clearboth" />

				     </div></a>

				   <?php endwhile; wp_reset_query(); ?>

			<br class="clearboth" />

</div></div>

 <?php  }

			?>

The operator AND function doesn’t work, I get no posts at wall while changing that one.

Grateful for help!