I'll abstain from the main topic for now, and skip to the extra credit. Since typewriters and computer keyboards don't generally have separate keys for hypen and dash, I was taught in typing class to indicate a dash with two adjacent hyphens. As far as I know, the only purpose of "--" in typed text is to substitute for a written dash. I would never use two marks like that when handwriting.

And for good measure, I'll mention that the difference between hyphen and dash should be the difference between night and day. It bugs the hell out of me when people use a hyphen (with no surrounding spaces) instead of a dash (with a space on either side). For example, they'd write your sentence as "... that directly-and potentially both positively and negatively-relates to ...". The hyphen serves to pull words together; the dash sets them apart. When people use the wrong one, they give the wrong indication of how the sentence is to be read. And yes, I have been genuinely confused in the past by sentences that make this mistake.

from my understanding of the that/ which issue, your usage is entirely correct, and the only reason i can see for your frustration would be the fact that you have a parenthetical before the second phrase using the word that.
read the sentence without the parenthetical and see if it still sounds awkward to you. to me, it definitely doesn't.
beyond that, i honestly can't elaborate on the your usage question . . . it's one of those things i suppose you get a feel for and beyond that, there's really no absolutely clear way to differentiate. i recall at one point when i was in school having explained to me that "that" is to be used with objects and "which" with subjects, but i never really found that to be 100% true, either . . . and beyond that, i recall another teacher trying to explain to me that "which" is to be used with people and pretty much nothing else while "that" can be used with just about any noun. this never seemed to be true all the time either, so i basically just gave up and let my instincts guide me with respect to the that/which issue.

regarding your "extra credit," there are actually _two_ types of dashes. the en-dash, and the em-dash. the en-dash is the single dash, and the em-dash is the double dash. as far as i can tell, the first signifies a brief pause while the second signifies a longer one. with that in mind, i've always been cautious to use the en-dash as a means to separate out a phrase [i.e., one at the beginning and one at the end of a phrase] while i've used the em-dash like one might use a semicolon. i personally have always considered the en-dash to be very useful, but as far as the em-dash is concerned, i think it can easily be replaced by the semicolon.

oh, and for good measure, the reason that they're called the en and em-dashes respectively is because the first is a single dash the width of the letter n, and the second the width of an m.

~e.