I have a security token question:

I have two accounts bound to the same token. When I login to the game, I'm asked if I want to use Final Fantasy XIV 1 or Final Fantasy XIV 2. If I want to use a different on only ONE of those accounts, is that possible?

And no, I'm not trying to transfer an account. I'm tired of passing the security token back and forth with my wife when we login to the game or forums or SE management account :P