Hello Jack2020,
I understand that you are not changing domain name, just changing physical location and now a new domain controller in the new site will connect your users to the SAME domain. So no need to run the deployment wizard to map the existing users to the new domain.
When moving to the cloud or a remote location, you will need that your users now login using IFD (Internet Facing deployment) so each user will need an Internet connection and now they will login using a "Login form" where they will need to write their login credentials to access the CRM server.
This setting is laborious but straight-forward, this is documented starting here:
docs.microsoft.com/.../dn609803(v=crm.8)
Notice that if you did not have IFD before, you will need an ADFS server and a public SSL certificate.
I hope this information helps!