If you want a nested child page to load when the home page is called, I would set up a separate page as your home page. Create a custom template for that page. Then setup a redirect in the template file for the home page.
You would then setup your placeholder page as the home page from the Settings->Reading menu.
So for example, first I would create a new template file that looks something like this:
<?php
// Template Name: Redirector
$redirect = get_bloginfo('url').'http://www.example.com/parent/child/'
wp_redirect($redirect);
exit;
?>
I would then create a new page. Name it ‘Redirector’ or whatever and then select the “Redirector” page template from the template drop down menu, which should be available on the page editor in the far right column.
Then you’ll need to select the “Redirector” page as your home page from the Settings->Reading menu. Select “Static Page” and then select “Redirector” as your Front Page option from the drop down menu.