Why does "Read more" link not show up on view, but "Add new comment" does?
You have a mistake on your code. Instead of $variables['content']['links']['node'] you wrote $variables['content']['links']['comment']. 

Corrected code:

function ap_hogeschool_theme_preprocess_node(&amp;$variables){

  $variables['content']['links']['comment']['#links']['comment-comments'] = FALSE;

  if( $variables['type'] == 'wie_zijn_we_' &amp;&amp; $variables['view_mode'] == 'teaser' ){

     $variables['content']['links']['node']['#links']['node-readmore']['title'] ='&lt;div class="custom-add-read-more"&gt; &lt;/div&gt;';
     // Mistake was in this line:
     $variables['content']['links']['node']['#links']['node-readmore']['html'] = TRUE;
     $variables['content']['links']['comment']['#links']['comment-add']['title'] = '&lt;div class="custom-add-comment"&gt; &lt;/div&gt;';
     $variables['content']['links']['comment']['#links']['comment-add']['html'] = TRUE;

   } 
  }