Nested tmux sessions on local and remote servers - nested

Question

I'm trying to setup tmux to work like so:
Outer session (level 0) on localhost with prefix C-a
Inner session (level 1) on localhost with prefix C-b
Inner session (level 1) on remote host with prefix C-b
So each inner session is nested directly in the outer session.
If I setup my .tmux.conf like this:
unbind C-b
set -g prefix C-a
bind-key -n C-b send-prefix
the local inner session receives the C-b prefix properly, but remote inner session doesn't.
If I change my tmux.conf to this:
unbind C-b
set -g prefix C-a
then the remote inner session receives C-b, but the local session doesn't.
Is there a way I can configure tmux so that both the local and remote nested sessions receive the C-b prefix?

Answer 1

Inspired by this blog post on Tmux scripting, I was able to find a solution. I put this in my shell startup script (e.g. .bashrc) on my localhost:
tmux_outer() {
SESSION=$1
tmux -2 new-session -d -s $SESSION
tmux set prefix C-a
tmux -2 attach-session -t $SESSION
}
tmux_inner() {
SESSION=$1
env TMUX='' tmux -2 new-session -s $SESSION
}
and removed my .tmux.conf
The problem in my original .tmux.conf:
unbind C-b
set -g prefix C-a
bind-key -n C-b send-prefix
seems to be set -g prefix C-a, which globally sets the prefix to C-a. In my shell function, I create the outer session in a detached state, set the prefix to C-a only for that session, and then attach to that session.
When I start an inner session on my localhost or remote host, it has the default tmux prefix C-b. Since the outer session isn't trying to capture and send C-b, both inner sessions receive C-b with no problem.

Answer 2

tmux manual says, if I read it correctly, 1) prefix is server-level setting and 2) all sessions are managed by a single server. This means you can't get outer and inner session at the same host with different prefixes, unless you are starting multiple servers using corresponding options as non-default socket and another config for a second server.
Alternatively, it's easier to use GNU screen instead of tmux. It allows prefix specification in command line and unlimited server count in a easier way.
UPDATE[2017-07-05]: modern tmux has enough per-session configuration, including switch prefix, despite in somewhat cumbersome way.