Display Child Page with custom fields within Parent Page

Your problem is that you are putting the page result in $page. While the normal commands like the_title() and get_field() will look for the $post variable if you are not setting a seperate ID of which you want the title.

I once did this by creating a backup of the $post variable, and then just put each post i wanted to include on the parent page in the $post variable. Then included the .php files, and every normal command like the_title(); & get_field(); works like it would normally would. But this is dirty, and there is probably a much better way to accomplish this.

You should probably just replace the main query with your get_posts query. Afterwards you should reset & restore the wp_query.

An other option would be to alter the page-customfield-3.php to include the $page variable you are setting in your page-parent.php.