query pages by a childs publish date

I am currently working on a wordpress project and would like to know if its possible to query pages by a childs publish date?

I currently only want to show the parent page so my arguments look like this:

$args = array(
      'post_type' => 'support_tickets',
      'numberposts' => -1,
      'orderby' => 'date',
      'order' => 'DESC'       
);

Is there anything i can do to adapt the above to order by the latest child publish date? I have already been down the route of using comments, but this is not going to work for what i want.

Has anyone achieved this before? Any help would be greatly appreciated