You can easily add a dynamic login / logout button to your menu bar and redirect users to a custom URL when they login / logout.
The easiest way to do it is using the Login or Logout Menu Item plugin. You can download it here.
Once the plugin has been downloaded and is active, go to Appearance -> Menus in WordPress to add the Login / Logout button.
Click the Login / Logout tab to expand it and select which menu point you'd like to display. Then click Add to Menu.
To redirect your students to a custom URL upon login / logout, please follow the instructions described in The Simple Way section of this documentation.