You could have all three showing in one terminal window (no tabs) with TMUX.
A terminal multiplexer would be the easiest way to accomplish this and automate it. After installing TMUX, create file that will hold the directives (this does not need to be executable). The contents of the file can change when you become more familiar with TMUX.
new-session -s workspace -d
split-window -v -t workspace
split-window -h -t workspace
select-layout -t workspace main-horizontal
send-keys -t workspace:1.1 'ssh webserver.fqdn' C-m
This will create your TMUX session, split into three panes in the same window, change the layout, and then ssh into your webserver in the first pane of the first window. To launch:
$ tmux -f ~/path/to/file/above attach
Controlling this session is much like
screen in that it has escape sequences to send commands to tmux in order to attach, move between panes within the window, moving between windows, etc... Full use/customization of this environment is beyond the scope of this question. I highly suggest reading the documentation.