Suppose we have the following situation: there's one network with a router on which the internet access is configured and this includes the DNS IP's. Then we set up Active Directory on a server on this network and promote it to a domain controller.
When I did that the only way other computers could be included on the domain created was by setting one of their DNS IP's to point to the domain controller. When I did that I was able to make the computers part of the domain. On the other hand, this made those computers stop receiving the DNS address from the router and so they couldn't navigate on the internet.
The solution I found was to add as secondary DNS address on the computers the first DNS address configured on the router. I personally didn't like this approach because of two things:
The DNS was set up manually in every computers. For just a few it is fine, but if there are many computers this is tedious and if one needs in the future to change this setting would need to change all the computers.
The only DNS address I could set up was the primary one. The secondary one, found on the router, cannot be used on the computers, because the two available ones are already in use.
So I think this solution is not a good one. How can I correctly set up computers in a domain to use the right DNS entries to navigate the internet and still be able to join the domain by pointing the DNS entry to the domain controller?
I assume you're using DHCP, right? Use DHCP to specify the default gateway and DNS servers. You can even use DHCP on your DC and keep it all in one place.
DNS should be provided by the domain controller(s). They can forward unknown requests to your ISP's DNS servers.
Basically, nevermind if your are using DHCP or not.
Using a single DC in your domain, you have to make it a DNS Server also. Install and configure DNS role on your Domain Controller.
Then configure your clients' DNS to point to the IP Address of your DC.
The most important thing is that you have to setup your DNS Server to forward unknown names queries to your ISP DNS Servers :
(just a screenshot from Google image as my interface is in French...)