Please clarify. Are you saying that you want to set up a restriction so that contact 2 cannot receive emails for cases 1,2,and 3? Not sure how that can be done, as a user can send an email to anyone and can set it regarding any case.
Or are you saying that you want to associate a specific customer with a specific case? You could do another relationship between case and contact and call it something like email contact, then you could trigger workflows to email this specific person when the case is updated.