We'd like to prevent certain users from being able to navigate to the "Network" browser to be able to see other computers... I was able to remove "Network" from Explorer in the left navigation pane, but you can still click in the navigation pane (via the breadcrumb links) and go to parent directories and eventually make it up to Network.

By disabling "run", it makes it so that a user can't type in a new location in the navigation bar... so is there any way to make it so they can't use the navigation bar to navigate elsewhere as well?

This is with a 2008 R2 domain.