Carousel Loop only duplicating

You should reset the query after your active slider.
So place this code after your first loop (after endwhile; endif; ):

//Reset Query
wp_reset_postdata();

Also try setting the paged atribute:

$paged = ( get_query_var('paged') ) ? get_query_var('paged') : 1;
// WP_Query arguments
$args = array (
    'post_parent'            => $destination->ID,
    'post_type'              => 'page',
    'posts_per_page'         => '4',
    'paged'                  => $paged,
);

Hope that helps,
Cheers