Hi Linda, I meant with Goldberg Sensei! That's where you train, correct?
gyaku means "the other way" (as opposed to the normal way) rather than the positional/geometric opposite
That's how I think of it for this aikido style!
And, I think it makes sense in this particular way for both the stance and the grab:
Grabbing a person's front hand (that's the hand you generally are after, if you're not coming from behind, yes?) is simplest if you are lucky enough to be on the guy's "outside" right? So that one gets the unqualified "katate dori" name in this style. It's the most straightforward single-hand grab, so no qualifier. But, grabbing that front hand from ai hanmi is a bit special, because the centerline is right there in your way.. better attackers than me can speak to the martial logic but you can probably see that this is less simple if talking about a real dangerous target. So, this gets the "reverse" terminology-- "gyaku."
So although there is logic in naming both the stances and the grabs using the "gyaku" term, it terns out weird:
-gyakute dori is done in ai hanmi
-katate dori is done from gyaku hanmi