Say I launch a program from the program I make. Is it possible to trick the launched program into thinking the windows directory is in a different place?
It would be difficult. There are several system APIs which the program might be using to determine the path of the windows directory. To trick it you would need to intercept the program's calls to whichever API it is, and return a different result.
There are many articles about intercepting APIs on Windows: here's the first one I found using Google: API hooking revealed.