Multiple Conditions for Child Page Title

I’ve been trying to work with Conditional Tags and cannot wrap my head around this problem. PHP novice here.

On sub-pages I need to display the parent page title as well as the page title. I have it working with this:

<h1><?php echo get_the_title($post->post_parent);?></h1>
<h2><?php the_title(); ?></h2>

But the problem I have now is that on the parent pages the page title is displayed twice, as the parent page title and the page title. Instead, when on a parent page, I need the h2 to display “Select a sub-page”, if there are child pages…or display nothing, if there are no child pages. Something like this is what I’m thinking is possible:

<h1><?php echo get_the_title($post->post_parent);?></h1>
<h2>
  <?php 
    if is_parent_page_without_children() {echo '';} ;
    elseif is_parent_page_with_children() {echo 'select a sub-page';} ;
    else the_title();
  ?>
</h2>

Based on the comment exchange, here’s what I think you’re after:

<h1><?php echo get_the_title( $post->post_parent ? $post->post_parent : $post->ID ) ?></h1>

<?php if ( $list = wp_list_pages( "echo=0&child_of=$post->ID" ) ) : ?>

    <h2>Select a sub-page</h2>
    <ul>
        <?php echo $list ?>
    </ul>

<?php elseif ( $post->parent ) : ?>

    <h2><?php the_title() ?></h2>

<?php endif ?>