The answer to this problem for terminator and remote systems is to create a terminator profile, where the command it runs 'as a login shell' is the SSH connection string used to access the remote server. It is prefered to have SSH key based authentication or openssh controlmaster/controlpath setup to have connection sharing.
Exerpt of a terminator config for this:
~/.config/terminator/config
[profiles]
[[default]]
scroll_on_output = False
exit_action = restart
scrollback_infinite = True
[[remotehost]]
use_custom_command = True
exit_action = restart
custom_command = ssh user@remotehost
And simply run terminator -p remotehost
to use this profile. Each time you 'split' terminals, it uses this profile and thus opens a new SSH connection.
For ssh controlmaster, see:
http://www.debian-administration.org/articles/290