But "arrive" isn't very old-fashioned, so translating it with an old-fashioned word would be out of place. You're saying don't use "прийти" in the situation I described, use явиться/появиться, instead? She was going to "appear" today at her new workplace? (obviously the literal English translation failing in this instance)
I think most native English speakers would disagree with your second sentence, which is probably part of the confusion. Of course, this in and of itself is far from dispositive; we are translating a very specific Russian verb. You're certainly correct that "arrive" in conjunction with "today" ordinarily refers to long-distance travels, for which "прийти" would naturally not fit.
I don't get what is specific about the Russian verb приходить, if it simply translates as to come, not as to arrive. There is no correlation and dependence between the verb to arrive and the adverb today. It seems you dig a little too deep ;)
To your reply below. I've mentioned already that the Russian equivalent of to arrive in the examples given by you below is a very formal/old-fashioned verb "прибывать". I can hardly imagine the situation it would be used in the major sentence of discussion. And I've given you much more usable synonims as to show up, to turn up and to appear. They have different translation (generally - появиться), but would work as the synonims in this particular case.
For example, I would say, "I was going to do that yesterday" in situations where I would be very unlikely to say, "I intended to do that yesterday" or "I planned / was planning to do that yesterday." Certainly the meanings tend to coincide, but "intend" or "plan" add a certain nuance that "going to" lacks.
My impression is that "собираться" is more generalized in use than "plan" or "intend" but not quite so much as "going to," which seems to be further down the path of taking an "actual" verb and "wearing down" its specific meaning to become merely grammatical in nature. I don't think the same phenomenon applies to "plan" or "intend." If you "planned" or "intended" to do something, you really did have to "plan" or "intend" it, but if you were "going to" do something, you need not have actually been "going" anywhere.
(None of this is to opine on the acceptability of "intended" as a translation here; I don't know/recall how that's handled in the course. If it's accepted elsewhere for "собираться," I don't know why it wouldn't be here.)