Windows – cannot add Windows 2016 to existing domain. Both domain and tree funtional levels are 2003.

You are probably trying to use a group that does not have the proper scope to see the members from the trusted domain.

If this is a cross forest trust the only type of group you will be able to use to assign users from domain b permissions in domain 'a' is a Domain local.

If this is not a cross forest trust then you can use Domain Local or Universal.

Microsoft has a good Technet Article about group scope.

Before you can add a Windows 2003 or 2008 domain controller (DC) to a Windows 2000 Active Directory you need to run the adprep /forestprep on the forest and adprep /domainprep on the domain in the forest where you'll be adding the new DC. A review of Microsoft's documentation of the process is probably in order before you start.

You do not need to install any Windows 2003 DCs prior to installing a Windows 2008 DC. You need only prepare the AD with adprep. Once you've done that you can begin to promote W2K8 DCs.