A. This isn't a SQL issue, it's an NT one. If you are using a net-lib that requires NT authentication - e.g. with 6.5 and below named-pipes or multiprotocol - then you MUST be able to authenticate to the copy of NT running SQL Server. With 7.0 all net-libs require NT authentication.
You can test whether you can do this by doing a "NET VIEW \\servername" from a command prompt on the client. If you get an access denied message, or get prompted for a password, then you aren't being authenticated.
If this happens then you need to setup a trust between the domains. Or, you could use a net-lib that does not need authentication - e.g. tcp-ip sockets.
If you can't have a trust (and really this IS the best method) then you can override the NT details by doing a "net use \\<server>\ipc$ /user:<serverdomain>\<userid> <password>" with an account that is in the domain. But this is a manual process and prone to fail when the password changes.