If you prefer to keep using the router as a DHCP server and you cannot customize the DNS setting on the router DHCP server, here's what you can do:
1. On the DNS server running on the Domain Controller, set the Fowarders to your router (192.168.1.1). You get there by right-clicking on the domain controller name in the DNS management console and right-click > Properties > Forwarders tab. This will allow the DNS server on your domain controller to resolve domain names that are on the internet and not in your Active Directory.
2. On Windows workstations, you can leave the IP address setting on Automatic (DHCP) but enter a static DNS, in your case, 192.168.1.10. This will make the workstations use the DNS server running your domain controller.
3. Now when you join a computer/server to the Active Directory, their host name can now be automatically resolved by any workstations using your domain controller DNS server (192.168.1.10).
4. If you have a host name that you need to create manually, you can edit the DNS server record and enter it manually. To do this, open the DNS server management console, open the Forward Lookup Zones tree, right-click your Active Directory domain and select New Host. You can then manually add in the desired host name and the IP address that it should resolve into.
Note:
If you just changed the DNS setting on the workstation, you might need to flush the DNS cache. Open a command prompt (admin mode) and enter: ipconfig /flushdns
1. On the DNS server running on the Domain Controller, set the Fowarders to your router (192.168.1.1). You get there by right-clicking on the domain controller name in the DNS management console and right-click > Properties > Forwarders tab. This will allow the DNS server on your domain controller to resolve domain names that are on the internet and not in your Active Directory.
2. On Windows workstations, you can leave the IP address setting on Automatic (DHCP) but enter a static DNS, in your case, 192.168.1.10. This will make the workstations use the DNS server running your domain controller.
3. Now when you join a computer/server to the Active Directory, their host name can now be automatically resolved by any workstations using your domain controller DNS server (192.168.1.10).
4. If you have a host name that you need to create manually, you can edit the DNS server record and enter it manually. To do this, open the DNS server management console, open the Forward Lookup Zones tree, right-click your Active Directory domain and select New Host. You can then manually add in the desired host name and the IP address that it should resolve into.
Note:
If you just changed the DNS setting on the workstation, you might need to flush the DNS cache. Open a command prompt (admin mode) and enter: ipconfig /flushdns

NS" in CMD as administrator - Failed to connect. Could not run LDAP, no error message given. I then tried "PING DOMAIN.LOCAL" - Could not find server, no response, timeout, etc. Then tried "NSLOOKUP 192.168.1.3" - Server unknown. Active and found, but no name. 

Comment