- Remove any and all public DNS servers from your DHCP scope. Internal DNS clients should only be using internal DNS servers for name resolution. You can configure forwarders or use the root hint servers on your DNS server for resolving external DNS names.
- Set up forwarders in your local DNS servers, so that they'll answer from local zones if they have them for a given request, and forward to internet servers if they don't.
Note: Adding external DNS servers to your DHCP scope isn't going to help, it's only going to create other problems for you. I can't tell you how many times I've resolved flaky email, internet, name resolution, and general network problems by removing public DNS servers from clients that should only be using internal DNS servers.