It’s got nothing to do with the router.
I assume that you are using the router as your DHCP server? I also assume that the router is using your ISPs DNS servers as the DNS servers to give you all your machines?
You need to remove all the machines from the domain, install the DNS service on the server, make sure that the server has it’s own IP setup for the DNS server (with no backup DNS server). Then configure the router to use the servers IP address as the DNS server with no backup DNS servers. Reboot the workstations to get the updated DNS information (or do an ipconfig /release and then ipconfig /renew on each machine). Then add the machines back to the domain.
If you have AD installed, you are using DNS from somewhere (installed with AD maybe?)
I agree with above, set DNS in the router to point to your DC. You might also consider moving DHCP to the DC as well. This can provide more security control than letting the router manage the address space. If you run DHCP from the server, you can reboot the workstations and get new addresses and also DNS registration. Once reconfigured, verify the netlogon share and sysvol are visible on the network and that GPOs propagate