In terms of "relationship," I would look at this more as to how they got along rather than how they were "related." There seems to be no connection in terms of Zeus being Prometheus' father, etc. (though it would seem that Zeus really got around).

The connection is more that Prometheus gave humans fire (stealing it from Zeus) because he felt sorry for them. This way they could have light after dark, be warm and cook their food. However, it was seen as an affront to the gods, for once mankind had fire, they were less dependent upon the gods...perhaps even more god-like themselves...or so the story goes.

And so Prometheus was punished, chained to a rock so that an eagle was able to eat his liver each night. The next day, the eagle was back and so was Prometheus' liver. The theme of repeated punishment is not isolated to this story. Eventually, Hercules rescues Prometheus.

The only connection between Prometheus and Zeus is that Zeus is furious when Prometheus helps mankind in giving him fire.

I don't think they were related either, except vaguely in that all of the Gods were related.  Even if they were, Zeus does not strike me as the sympathetic sort.  He needed to make an example of Prometheus, and found a grisly but effective way to do it.  How else do you punish someone who's immortal?

I agree with #2. We have no information that claims a kinship between Prometheus and Zeus, apart from their shared identity as Titans. As Zeus was the leader of the Gods, he had the right to be obeyed, and therefore the right to punish any Titan that disobeyed him. Prometheus, whatever his motives, did disobey Zeus, and so he was punished accordingly.

I don't think that Prometheus and Zeus are related, are they?  Prometheus was a Titan and Zeus was, of course, an Olympian god.  These groups were not related and in fact they fought each other for supremacy with the Titans losing to the Olympians.  So I don't really think there's any inconsistency with Zeus being so vengeful.