I would suggest 3 boxes. You have the alpha.com master domain controller
already. Build the new internal.alpha.com on a new box and migrate the
beta.com folks to internal.alpha. Take the old beta.com DC and build a new
external.alpha.com, then migrate alpha.com down to external. Now the box
that i
Although you give both the pre and post states domains in fully
qualified formats and not NetBIOS it is not clear if the existing
accounts domains are already AD? If not the clear path to minimise the
impact to users is to migrate the domains to a new forest i.e. Create
your 3 domain forest struct