By targeting Michael (and if his role was discovered), Barzini could expect to earn whatever wrath Vito could muster - and if Vito was unhealthy he could even trigger a transfer of power to Clemenza or Tessio, who might be easier to deal with. By targeting Apollonia (and if his role was discovered), Barzini could expect to earn whatever wrath Vito could muster, plus vendetta from Michael, plus a loss of all support from other families, because he targeted a civilian family member. I don't see how that calculus works in favor of targeting Apollonia.
Very good analysis, mustachepete. That's one avenue I hadn't explored of the scenario. In committing such an infamita, Barzini would definitely risk the loss of support of the other families if they get the idea that he went after Apollonia as a way of breaking Michael. If he was after Apollonia, it was a genius plan as Michael said in the belief that the bomb was meant for him. Not even Vito would've known better. In that case, Michael didn't know better either.
In that scenario, if Barzini succeeds in taking out Michael, that would only leave Fredo as Vito's only remaining biological heir. Vito likely goes to war in that scenario. It makes me think of this: if Vito wants to go to war, would Tessio make the same play with Barzini as he did when Michael was in charge?
Either way, Barzini's tactical error was calling a hit in Sicily and having the attempt made after Vito called the peace talks. If it succeeds (taking out Michael and/or Apollonia) and he gets found out, it's war. If it fails and he's found out, it's vendetta.
