Does tmux integrate with itself? That is, does this solve the problem of needing different prefix keys when nesting tmux sessions (whether using iTerm2, or using a terminal emulator that doesn't itself integrate with tmux)?
For me personally, I use ctrl-a instead of ctrl-b so I have this line in my ~/.tmux.conf:
#send prefix to nested sessions with C-a
bind-key C-a send-prefix
I take it with nested tmux sessions, cmd-D would split the outer tmux window? How would you split the inner tmux window?
It's worth checking your config file out.
And I'm not sure how to answer your question because the way iterm integrates with tmux is that it allows you to create split panes with their own bash sessions. If you want to run tmux in those sessions, it would be tmux running in that pane, but textually instead of graphically. Here's a screenshot to make things more clear: http://i.imgur.com/0hmw62I.png
cmd-D would just create another pane to the left.