Hide "Add Relationship" Button
Not sure what CMS you're using - it would be nice if you could permission this but I can't in WordPress so I see the need you have.

Just add the parent selector as well:

.contact-summary-relationship-tab .action-link
(the parent id an ID not a class but when I place the pound sign it thinks it's formatting)

Keep in mind, there is still an option in the actions menu as well that you'll want to hide.