Active Directory, Domains, and NAT

Here is what I have:

Some computers as
MACHINE1.SUB.DOMAIN.NET
MACHINE2.SUB.DOMAIN.NET
MACHINE3.SUB.DOMAIN.NET
In which I do not control the DNS, but an existing Active Directory Forest exists as:
DOMAIN.NET but no Exchange server exist or Active DNS, only legacy Unix DNS/Email.

I also have machines in a nat on
MACHINE4.SUB.DOMAIN.NET
as
MACHINE4.HIDDEN.NET

I also have an exchange server 5.5 on the border.
MAIL.SUB.DOMAIN.NET
and
MAIL.HIDDEN.NET

I want to moveto Active Directory inside the firewall and move the Exchange server off the border to inside and upgrade to Exchange 2000.

How do I get Exchange to work properly inside as outside. (MAIL.SUB.DOMAIN.NET & MAIL.HIDDEN.NET or MAIL.LOCALHOST or whatever…)

What should I need to name my Internal Domain/Forest?