How are users connecting to the database now? If it is by Windows Authentication, that might break. Both domains have to be trusting of each other. In other words, users on both domains need to be able to authenicate via the same domain controllers. Normally, the domain controllers are replicating logins to each other.
You may need to make the services domain accounts.
Is there a firewall involved? If so, is it open to the ports being used by SQL Server?
Are the physical servers being moved or only the databases?
-SQLBill