The app is constructed so that the user first encounters a login page where he can enter his username and password, and the name of the server he wants to work on, [...] I use (abuse?) Dancer2's session mechanism to store all the relevant data from the server the user working on - and here is my problem. Dancer2's sessions are, in effect, per browser.

Your problem is your login page. Dancer2's session's aren't per browser. They are per browser, server, and TCP port. If Dancer2 uses cookies for storing a session key (most likely it does), you can set the cookies for a subtree of the document tree. So if you construct your URLs to look like http://loginserver.example.com/session/littleserver/..., http://loginserver.example.com/session/bigserver/..., http://loginserver.example.com/session/otherserver/..., and so on, and set the cookies path to include the server name (i.e. /session/littleserver, /session/bigserver, ....), Dancer2 should not confuse the sessions.

Alexander