I have two computers in a workgroup. I connect to the 2nd computer
from the first (as a mapped network drive) and accidently delete a
critical folder with sensitve data. The folder is not in the recylce
bin of either computers. How can I completley retrieve my data?

George Skarbek who writes a column for a number of large Australian
daily newspapers answered a very similar question that I saw published
this week. Unfortuneately I can't see that his answer is on his
web-site yet.
http://www.skarbek.com.au/

"When a file is deleted it is not physically removed from the disk but
its name is changed so that the space occupied by the file is then
available for overwriting. It may be possible to retrieve it by buying
specialised software if this space has not been re-used."

George went on to say that there are many programs that claim to
recover deleted files but no such program in any version of Windows.
(i.e. No such program comes from Microsoft as part of Windows)

Personally I have a program pre-installed onto my computer as part of
Symantec's "Norton" suite of programs called "Norton Unerase" however
I know that program MUST be there beforehand to keep a log/list of
deleted files as they occur otherwise I believe it can't be loaded
after the event to trace previously deleted files. The program further
'protects' a quantity of the most recently erased files. The program
has been reasonably successful for me.

George said he had not tested many of the programs and suggested (not
recommended) trying "O & O Unerase" as apparently the trial version
will show what files can be recovered but not actually do the recovery
so you could find out if the program will do the job for free and, if
so, then pay for the full program activation.
www.oo-software.com/en/products/oounerase/index.html

I looked at this web-link and see the product claims "O&O
InstantUnErase for Data Recovery without any pre-installed software"

By the way, I believe the remains of the deleted files will still be
on the computer they were stored on and not on the computer which sent
the delete command.

Finally TIME is CRITICAL here. If the erased files have already been
over-written by other files then you won't be able to recover the
files. Because the Operating System considers the space previously
occupied by the erased files is now available for use it may overwrite
the space at any time. If the files are "critical" then STOP using
that computer until either you or if necessary a professional has a
chace to try and retrieve the files for you.

spelling correction "chance" not "chace"

...has a chance to try and retrieve the files for you.