I was able to login as
http://<domain_name>:3000
Done some import jobs, publish the map, copied the API link to a sample HTML page. Able to view the whole base map and CartoDB layer from local. But I tried from other network, the CartoDB layer seems to be not seen. Checked the console, but no errors where logged. Edited the development.js from the Windshaft directory and changed the localhost instances to domain name, and also the app_config.yml files.
The local system browser knows about your domain just because you've added an /etc/hosts entry pointing domain to your localhost.
I see two ways for you to see your cartodb from a remote network:
a) accessing your computer using it's public IP, like this: http://public_ip:3000
b) having access to your DNS server and inserting Address records for your domain and for your subdomain, like this:
NAME TYPE VALUE
--------------------------------------------------
domain.com A public_ip
subdomain.domain.com. A public_ip
This way, you'll be able to access your machine from remote using http://domain.com:3000
See also, this link.
