One domain multiple subnets

I have a domain controller on one subnet and want clients on another subnet to logon to the domain controller
in the other subnet.
I want some users to access the internet and deny access to others. However, if I remove the gateway from the remoteclients I don’t want having internet access then they are not able to logon to the domain controller that is not on their subnet.
How can I route the clients to the DC without assigning a default gateway?
I need to know the router configuration and client configuration to make this work.
Thanks
David