How to split screen in TotalTerminal to end up with two terminals?
The way I achieve this is ensuring that tmux is installed on the machine I'm SSHing to.

Once you've issues tmux you can do ctrl-b % to split the screen vertically, or ctrl-b " to split it horizontally. 

This will give you two sessions within the same terminal window, and can also be persistent across logins. This may not be exactly what you want though.