If you haven't mapped Ctrl+b Ctrl+b
If you haven't mapped Ctrl+b Ctrl+b to last-window to emulate screen's behavior (which is quite popular), then you can use that as your prefix for the inner tmux session. So to issue commands to the inner session you would use Ctrl+b Ctrl+b Command
The above answer assumes your prefix key is still Ctrl+b on both machines.
If you have mapped Ctrl+b Ctrl+b
If you have mapped Ctrl+b Ctrl+b, then you'll need to use tmux's
:send-prefix command. Many people map this to Ctrl+b b to emulate screen's default behavior. You would add this to your .tmux.conf to add this binding permanently:
bind b send-prefix
Then you can issue commands to the inner session using Ctrl+b b Command
(or without the binding using Ctrl+b
The above answer assumes your prefix key is still Ctrl+b on the outer session.