Breaking up multiple words and inserting an image after first word

Assuming you know that there will always be two words separated by a space, you can use explode. Something like this:

$pieces = explode(" ", get_the_title());
$word1 = $pieces[0];
$word2 = $pieces[1];

$output .= '<li><a href="'.get_permalink().'" class="'.$page_id->post_name.'-link"><div class="'.$page_id->post_name.'-info"><h2>'.$word1.'</h2><div class="'.$page_id->post_name.'-img">'.get_the_post_thumbnail($page->ID,'icons').'</div><h2>'.$word2.'</h2></div></a></li>';