Thanks for all the input guys, MUCH appreciated! It turns out that it's even MORE complicated than any of the above, and involves both an OpenType and Type1 versions of the same font. :/
So, Windows has 2 registry areas that hold font info for PostScript fonts (OTF and Type1), more specifically, entries that "point" to font filenames. Various font management software only update the "Wow6432Node" registry entry, which seems to be a "legacy" entry that the Adobe apps (InDesign and Photoshop at least) do not "see," they only look at the newest registry entries. Which pretty much makes sense.
As a point of note: If the InDesign file being opened already has a Type1 font that is only in the legacy registry entry (the one InD doesn't "see") it will still use the font correctly. I THINK because the path of the font file is actually stored in the InD file (someone please correct me if I'm wrong).
At some point, on the computer that was displaying the no-break space the same size as the regular space, the Type1 font had been loaded into the registry key that InD can "see." When the OTF font was loaded on that computer InD was getting to confused because it had the OTF and some font cache stuff from the Type1 font. It was using the Type1 font metrics, apparently.
Which brings me to another point: InD does something different with the no-break space in OTF fonts than it does Type1 fonts. We discovered this by UNloading the OTF and putting the Type1 font files in the "C:\Program Files (x86)\Adobe\Adobe InDesign CS6\Fonts" folder. When using an OTF font and setting a no-break space, InD appears to use the width of the no-break space glyph (00A0), but when using the Type1 font it uses the width of the regular space for no-break spaces.
By unloading the font everywhere and deleting the InD font cache files all machines were setting the no-break space the same size using the OTF font. WHICH was actually the WRONG size, it was larger than a regular space! We ended up changing the width of the 00A0 glyph to match the regular space and regenerating the OTF.
Hope this helps someone, sometime.
All best and thanks again,
Ken