Parent and child pages in permalink

I want to display child page preview with excerpt on a parent page. The child page will always have the same title, but the parent will be different.

At the moment Im using this code:

$page = get_page_by_title( 'Child Title' );
 $page_excerpt = $page->post_excerpt;
<header class="wpb_wrapper">
    <h4 class="gp-element-title xcpt">
        <a href="<?php echo esc_url( get_permalink( $page ) ); ?>">
            <?php echo $page_data->post_title; ?>
        </a>
    </h4>
</header>
    <div class="gp-entry-content xcpt page-layout"><?php echo $page_excerpt; ?><br/>
        <a href="<?php echo esc_url( get_permalink( $page ) ); ?>">Read More...</a>
    </div>

This code sits in the parent page template and every time I create new parent page the parent link stays the same, but I want it take the slug from the new parent page. So for example now there is http://www.example.com/parent/child and when I create new parent page called “new parent” I want it to be http://www.example.com/new-parent/child.

Also the excerpt doesnt work and I have to manually enter the text into metabox in admin, is there a way to display the excerpt dynamically? Thanks for any help!