Are you trying to keep all the "session" type objects created from computerA?
If not, I have seen web sites do something roughly like this:
When a user logs in from a computer, somewhere in a table, information about that login is stored (the IP/MAC addresses perhaps?).
So then, when another computer attempts to use the same login credentials, the backend can see that a session from the first computer is still open (the user has not logged out and the session has not timed out due to inactivity).
The backend has two options to chose from now. It can either:
A) Inform computer2 that it cannot login with that user as the account is still in use on another system. Rejecting the login request.
or
B) Update the internal state with the information about the new login (IP/MAC sessionID, whatever) and tie it the user login. This would then accept the login and make it the active session for the user credentials. Any further attempt by the first computer would be met with "invalid session state" / "not authenticated" or whatever, and that computer would have to attempt to login again, repeating the process.
If you are trying to keep the session objects, I think you would have to do some "backend smarts" and check to see what session ID is associated with the user credentials requested, and return THAT sessionID as the sessionID for the current connection request (rather than create a new sessionID)