When you are trying to add remote site you get an error: Unexpected Status code: 403.
And it seems like that the vSphere Replication Appliance is not even trying to make connection with the remote site.
Remote side can be reside on a different vCenter in same AD domain or another AD domain.
1. Validate your internet explorer is not using any proxy settings.
2. Validate that the connection between the VRA and the remote vCenter is not using any transparent proxy.
3. Make sure the SSO is working properly on both vCenters
4. USE FQDN all over, that can be resolved on both sites, otherwise the pairing process will fail.