Wordpress - Adding a Template to the Page Attributes Panel for both Posts and Pages?

You're not doing child themes right. A child theme is a separate theme altogether that everyone must use, but relies on another theme for all template parts it doesn't provide. What you want is templates:

http://codex.wordpress.org/Theme_Development#Defining_Custom_Templates

Basically, just create a new theme file in the theme's root directory (e.g. foobar.php) write this at the top:

/*
Template Name: Foobar
*/

That will give you a new template called Foobar (obviously, change Foobar to whatever you want. That's the name that will appear in the dropdown menu on the editor page).

As of now, WordPress only supports templates for pages and custom post types, not posts. There are ways to hack this, like checking for a post meta on posts and pulling it on template include:

function my_post_templater($template){
  if( !is_single() )
    return $template;
  global $wp_query;
  $c_template = get_post_meta( $wp_query->post->ID, '_wp_page_template', true );
  return empty( $c_template ) ? $template : $c_template;
}

add_filter( 'template_include', 'my_post_templater' );

function give_my_posts_templates(){
  add_post_type_support( 'post', 'page-attributes' );
}

add_action( 'init', 'give_my_posts_templates' );

If you put that code in your theme's functions.php file, that should work (as long as you actually have custom templates in your theme folder).

For more information about child themes, read here:

http://codex.wordpress.org/Child_Themes

From wordpress 4.7+ you can put 'Template Post Type' in your custom template file to display it in page attribute for both page and post.

/*
  Template Name: Your Template Name
  Template Post Type: post, page
*/