This page states that you can not change your primary domain if you have Chrome device licenses.
With regards to multiple domains in general: first of all, you need to set up your 'alias' domain as a secondary, otherwise it will only be recognized by mail and DNS, but nothing else.
Next, there are a few options.
One is to promote your secondary (short) domain to primary. This will move all assets (mail, calendar, sites, whatever) that you had on the old domain to the new one. It will also perform a mass migration of your users from their current to the new domain. Since you have Chrome Device licences, this is not an option.
You can move users from one domain to another, however. This can be done in the Admin Console, but if you use GAM, you need to change the email and not the username:
For groups, same thing:
There are several ways to do this for lists of users or groups; refer to Wiki pages on 'bulk' processing.
--peter