Mi ne estas fakulo, sed mi pensas, ke ĉi tio estas ĝusta: I'm not an expert, but I think that this is correct:
Mi bedaŭras, ke miaj emocioj vin kolerigas. = I am sorry that my emotions anger you. (This can also be translated as "regret", so "I regret that my emotions anger you".)
Mi pardonpetas, ke miaj emocioj vin kolerigas = I am sorry that my emotions anger you[, will you forgive me?]. (This one is more directly asking for forgiveness, hence what I have added to the end of the sentence in brackets.)
Hope I helped!
I'm not entirely sure that it's a conditional. There are a few corner cases where "se" can show a cause more like "ĉar" and "ke." But, I don't entirely understand that part of PAG: "se, demanda-motivanta."
If this is "se motivanta", it means the same thing as this:
> Mi bedaŭras, ke mi ĝenas vin.
but with less certainty that I have actually bothered you.
> I am sorry since I may be bothering you.
It's not a way to dodge responsibility - I am apologizing for guessing your feelings too.
Here's the part I'm not sure of: the main clause must demonstrate conjecture on the speaker's part. The examples given use adverbs "sendube" and "eble." If this were expressed with an adverb... well, it would still need to be explained, but it would at least hint at this usage.
> Mi bedaŭras kaŭze/supoze se mi ĝenas vin.
This is (yet another) example of Esperanto being elegant and old-fashioned with its grammar.
It probably comes from the French verb "gêner", which according to Wiktionary means
1. to bother, annoy, irritate;
2. to hinder, hamper, bother;
3. to embarrass
It's also related to the German word "genieren" (meaning to be embarrassed or to embarrass someone else), which comes from the same French word.