It is very unlikely that you will get two servers in different domains (NT&W2k) working without setting up a trust between the two domains. Windows authentication uses a SID (security identifier) each computer and each user has a unique SID and the authentication should use the SID not the username. It is true to say that NT4 could be fooled depending on what service pack you used, but W2k with Active Directory will require a trust.
I recently upgraded a whole network of users from NT4 to W2k with AD in a different domain. I researched this and it will only work with a trust relationship as HMScott says. In our original plan we were going to use replication and migrate the users one by one, in the end we moved every9one ov
The way we get around such problems is to use a Role, we have one SQL username in the Role and have our application use that username. Granting ODBC connections may be quick and easy but it leaves you a bit exposed to other issues of Security & Support.
Imagine if this was not the case, any old hacker could access you databases.