Well, If I have a chance to react to that before your decision is final, I could say that if you do that then I'll go anyway (Thus leaving mother to burn) Then it seems to resolve to Chicken. (We both want the other person to back down first, so that we can go all the way to Olympos, but if neither backs down, mother burns in desert heat.) And if I don't have a chance to react to that before your decision is final, then it's sort of like "What do you do if you are playing Chicken against someone who has already smashed his steering column with a rock?" And I think that makes sense, since in both cases (blackmail, chicken) the goal is make the person back down because of some sort of threat. Does that help?

As I said elsewhere, I think identifying blackmail depends on identifying an agreed status quo state. This is fairly easy in ordinary life (if we had an affair, the ordinary human expectation is that you would keep the letters secret for free, etc.), but more difficult in outré cases like this one and the other one you suggest with the letters in the cave. It is not surprising therefore that in cases like this we do not have clear intuitions. That said, following the definition I proposed, I'd say that in your first example if it is a plausible status quo that your brother would go to Olympos (maybe he got a job offer letter form there?) then it is blackmail for you to go instead. If he just happened to come up with the idea of leaving, then my intuition is that this is not a plausible status quo; there is no stability, no ordinary human expectation that you would abide by his decision of leaving you stranded. A more plausible status quo (which applies also to the perfectly symmetric case when both come up with the idea together) would be flipping a coin to decide who leaves. Relative to this, either of you leaving is blackmailing the other.