Hi.
If Azure is going to be your second datacenter, you should allow authentication to Azure DCs also from onprem infrastructure. So if Azure is going to extend your onpremises datacenter, then you should interconnect those networks, so use either Azure ExpressRoute or site-to-site VPN. Then the infrastructure deployed in Azure will be part of your internal network.
You should never expose DCs directly to the Internet, DCs should be accessible only from internal network.