AD server within another network - DNS issues

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http://serverfault.com – Here's a quick summary of the environment I support: we have a domain (domain A) that has about 20 client computers. The domain server for this domain and all the clients sit within the network infrastructure of a larger domain (domain B). All the computers get their network settings via DHCP from domain B's servers. I have no control and am unable to make changes to anything to do with domain B. The problem I have is that currently in order for my domain's (domain A) clients to be able to resolve the domain server and the shares on it they have their DNS server IP address set to domain A' (HowTos)