Aight, I figured it out. Turns out I'm just an idiot who overcomplicated the whole thing.
Who'd have thunk it?
Solution: You choose the ship you wanna move on the Galaxy Map and then right-click on a sector in range.
Cheers.
So I got the quest from the Adventurer guy to make his ship "Lady Adventurous" jump to/back from a selected sector. I just can't seem to figure it out.
Please help if you know what I'm doing wrong (or rather not doing right). It's driving me insane.
Thanks!
/Torokin