Windows Server 2008 - Strange DNS resolution between clients and server

This behavior is expected given your configuration. You shouldn't have the router's IP set as the secondary DNS for PCs and member servers or they'll always sometimes go there which you don't want. They should only have domain controllers as their DNS so all of their DNS traffic routes through the domain controller. You can then either configure your domain controller to forward to an upstream DNS server for domains it can't resolve (usually this would be your ISP) or just leave it alone and it will use the root hints servers to resolve external queries.

Typically you would want two DNS servers on the PCs and member servers and you would get that by having a second domain controller so DNS (and Active Directory) continue to function if the primary goes down.

The first thing I would do is to remove the routers IP address from the DNS configuration on the clients (servers included). All AD/DNS clients should use your AD/DNS server for DNS only. I see no valid reason to use any other DNS server and can see that causing intermittent, flaky name resolution problems, such as what you're experiencing..

icky3000 hit the nail on the head. Your fallback proxy DNS servers are providing a different view of the DNS namespace to your principal proxy DNS server, and things are going wrong as a result. Don't do that.