Opening a new window, and cd to the same directory as the current window, no matter what I'm doing

Hello,

As the title says i'd like to find a way to open a new window and change 
its CWD to the same dir as the curent window (well the 'other' one once 
the new window is created)

So far, this is what I came up with:

=> I can issue:
    screen -X eval screen "stuff 'cd $PWD^M^L'" other

on the command prompt, and it works.
However, this obviously doesn't work if, on the current window, I'm on a 
remote box (via ssh...)

and as a minor problem, I can't find a way to bind this to a key:
  bind N stuff 'screen -X eval screen "stuff \'cd $PWD^M^L\'" other'

I got:
 : Missing " quote.

(I could make an alias, but I'd have prefered a 'keystroke')



Anyway, my point would be to have something like this working working no 
matter what i'm doing on the current window.

So.. a few more questions:

1) Is there a way for screen to know an environment variable value in 
one given window?
    if this is possible I could use screen to set this var: WOLDPWD 
(window OLDPWD) before the new window is created, and then in my 
~/.bashrc, I can check if this var is defined, and change directory if 
it is.

2) if answer to 1) is no, then is there a way for screen to know which 
tty is 'used/attached ?' on current window?
    Again, if is possible, then I could use screen to store this value 
in a variable, before the new window is created, and then in my 
~/.bashrc, I can find the process 'owning?' this tty, and find its CWD...

3) How is the current window number stored in screen? I mean, is there a 
command, a register or something, that would tell me the current window 
number? Then I could store it in a variable before creating the new 
window...

and... since on every window, the variable $WINDOW is defined (at window 
creation, I know, but I don't change the window number), in my 
~/.bashrc, I could find back the process with $WINDOW = current window, 
and then find its CWD



Ok that's a lot of questions I know, but this is the last bit I'm really 
missing in my screen conf :)

Thanks in advance :)

samlt

I thought may be screen could set en environment variable that says