link directly to custom post if there is only one in the taxonomy

How about doing it this way:

<?php
// Get (at most) 2 "product" posts in the child term.
$posts = get_posts( array(
    'post_type'      => 'product', // just change the post type if it is not "product"
    'posts_per_page' => 2,
    $taxonomy_name   => $child->slug,
) );

// If there's exactly 1 post, use the post permalink.
if ( 1 === count( $posts ) ) : ?>
    <a class="button" href="<?php the_permalink( $posts[0] ); ?>">See this Product</a>
<?php // Else, use the term link.
else : ?>
    <a class="button" href="<?php echo esc_url( get_term_link( $child, $taxonomy_name ) ); ?>">See this Series</a>
<?php endif; ?>