Instead of push segue how to replace view controller (or remove from navigation stack)?

Question

I have a small iPhone app, which uses a navigation controller to display 3 views (here fullscreen):

Answer 1

What you should really do is modally present a UINavigationController containing the social network UIViewControllers overtop of your Menu UIViewController (which can be embedded in a UINavigationController if you want). Then, once a user has authenticated, you dismiss the social network UINavigationController, showing your Menu UIViewController again.