A couple of questions are in order.
1) Do you use the same domain internally? It’s common for an enterprise to use “our_enterprise.local” inside and “our_enterprise.com” outside. If this is the case, then you’ll need to add a secondary domain to your internal DNS server pointing at your external domain controller, and make sure that the external domain controller knows that the internal DNS (or its translated address) is authorized to perform zone transfers.
2) If you use the same domain (our_enterprise.com inside and outside on different name servers), then you’ll need to maintain the DNS records for the web site in duplicate on each name server.
If you’ll write back with some more information about the structure (and PLEASE anonymize it) of your network and name servers, we’ll be better able to help.