There were issues with multiple Cygwin installations long ago, but I think they were corrected in the Nios I 3.1/3.2 time-frame... as such I'm surprised to hear that you ran into trouble with Nios II - perhaps something else is going on?
Just as a reference point, I personally use a generic Cygwin installation installed in a separate location from Altera's (which now goes into quartus/bin/cygwin)... in fact we (as Nios/SOPC developers at Altera) use a separate Cygwin installation extensively (on our desktop PCs as it provides a nice cross-platform development/build-system setup; so many people have this working.
The one tip that comes to mind to ensure that wires don't get crossed. I can think of two things: environment variables, and cygwin1.dll (there are a number of versions of it and you want whatever shell you open up to be using the most recent one).
I would carefully check that, when you open your Altera SDK shell, your environment variables & path do not point to your separate standalone Cygwin installation -- this is how things are on my setup. I also checked what my environment looks like with my standalone Cygwin installation, and to my surprise there were path entries pointing to the Altera installation of Cygwin. Everything functions normally, though.
You might also try a quick registry scan to see if there are any relics from the past floating about. In my working setup, I started from a clean PC with nothing on it, and installed Quartus and then Cygwin separately.
If this doesn't help feel free to send me an email offline and I'll send you a cut & paste of what my environment looks like.
Jesse Kempa Altera Corp. jkempa at altera dot com