|You need a VPN connection between the systems in the other states to the network where the DC is. Without a VPN connection from the systems in your other states, you won't be able to join your domain. You do not want to allow SMB, Kerberos, and all the other protocols needed to be NAT'd to your DC directly, without a secure tunnel (IPSec VPN) connection established first.|
As guapo said, don't use a publically resolvable TLD for your domain name. Use .local, or .lan, or anything else.
I guess, what is your ultimate goal you're trying to accomplish?