I think you may be confusing parent pages (hierarchy) with page slugs (the URL). Parent pages are designed to allow you to programmatically build things like menus/submenus and breadcrumbs. Whereas a page slug is the visual representation in the URL.
Many times, of course, I’d recommend you make your page slug match your hierarchy (for the user experience), so I think you’re half way there.
First ensure your permalinks are setup properly (system wide) in the Permalinks settings page:
Then in your child page, make sure the Permalink reflects the URL you’re hoping to display (it’s just under the page title).
Since you mentioned that www.mywebsite.com/Argentina/ works, I bet when you look at the permalink on the Argentina page, it’ll show the Permalink as http://www.mywebsite.com/Argentina/