You are correct that in your control panel, if you head to Website > Your site > Site settings > there will be a checkbox that says "Show parent in nav dropdown

If the parent page is still showing up in the top nav, under Site settings hit Clear cache. Often times when you make design changes (like changing top nav items) those will not immediately reflect. Clearing the cache is a good way to make sure you're seeing the most up to date version of your site. 

For the mobile version, this does not update and would need to be altered in the theme files of your nation. 

Follow these steps to create a custom theme. When you access the theme files, head to _nav.html > on line 15 you should see 

<li class="show-parent mobile-visible"><a href="{{ child.url }}">{{ child.name }}</a></li>

Remove that and Save and publish changes. You can also frame the line with {% comment %} {% endcomment %}