As far as personnal licenses go, you can use them on every computer you want as long as you are the only one using it, I would suggest either getting the license on a private usb key and placing it in your documents folder under your session, or simply set C2 so it looks for it inside the usb key
(One thing that can be done is to install C2 on said usb drive, and placing the license inside for convenience)
You can also I think get back a copy of your license from the store if you need (unsure if it still works that way as, well, the store was not the same when I got mine).