Wow! Now that is a really cool script. I'm not terribly suprised that I don't remember seeing it in the past; West African scripts are a weak point for me. If someone had told me that it composed like hangul I am sure I would have paid closer attention. :)
As far as this issue goes: I'd strongly suggest defining that non-whitespace single-dot word divider someplace that is not 0020. Fonts for scripts that have non-whitespace word dividers, like Ge'ez, typically encode them elsewhere. (x1361 “ETHIOPIC WORD SPACE”) Fonts that have spaces that would diverge significantly from a generic ASCII space (e.g. fullwidth and halfwidth spaces for East Asian scripts) also encode those spaces someplace that is not 0020. I'm no font designer, so I wonder what “best practices” are here, but I can't think of an argument against leaving the ASCII space for ASCII. Sorry, but it looks like we (“we” being “people who care about complex scripts” here) will be working around the ethnocentric assumptions of mid-20th-century computing wonks for, well, for as long as Western Civ exists.
I've just tested a custom font that contains ligatures and an outline in the space glyph and got the same problem in InDesign CS 5.5 as described by quinyu.
I can't see it as an InDesign issue, really; it's an ASCII issue, and you can expect other apps besides InDesign to be picky about what is encoded in ASCII. It's the kind of thing that software developers assume to be set in stone.
and you might need World-Ready Paragraph Composer turned on
Pretty sure that the Japanese composer will respect all of the relevant OT methods. :) However, quinyu, you should probably go and learn how to turn the WRC on and off so that people who aren't you might be able to use your font in non-JP ID at some point in the future.