Hello,
On your second computer simply install iLOK Manager then log with your credentials. Once logged you will see all your licenses.
Then go to File | Close all cloud sessions (if it is greyed out, it is ok, if not, then click on it). Finally go to File | Open my cloud session. You can now open Hauptwerk.
Should you want for some reasons use the original computer, you simply close and open a cloud session on the other computer.
Hope that helps