If there is no router between the two subnets, then yes, you would have to adjust the subnet mask to have all of the hosts be able to communicate with each other. Just by changing the subnet mask on this one client is not going to work. For example, if your client is on the 192.168.1.0/16 subnet, but you have a DC that is configured with 192.168.2.0/24, they will not be able to communicate because the DC will see the remote IP as on a different subnet and it will send the traffic to its default gateway instead of sending the traffic directly to the client.
You dont have to use a /16. Its fine if you do, but if this is part of a larger network, a /16 may conflict with other subnets on the network. You could also use a /23, but that would require you to have all of the hosts in this range --> 192.168.0.1 - 192.168.1.254.
If you need help with subnetting, you can use an online IP Subnet Calculator to help you figure out the best subnet addresses/masks based on how many IPs you need.
Do you mean join the Domain as in 'having a win client become a trusted domain member'? If yes, then follow JorgeM's instructions on getting subnets working first. Windows clients can join Win Domains regardless of subnets just as long as they 2 devices have ip connectivity. I've joined domains over VPNs and it works just fine.