Trying to display next and previous set of posts on separate page (not parent page)

what is not working with your existing code?

try to use:

<div class="alignleft"><?php  previous_posts_link('Previous',$loop->max_num_pages) ?></div>
<div class="alignright"><?php  next_posts_link('More',$loop->max_num_pages) ?></div>

and add <?php wp_reset_postdata(); ?> at the end of your code.