As we see in the movie and novel, Apollonia meets her untimely end via car bomb at the hands of Fabrizzio. The novel elaborates on this subject with Barzini being complicit in hiring Fabrizzio to carry out the job. At first, we're led to believe that Michael was the intended target of the bomb...but was he really?

In the movie, we see the car bombing scene just before the meeting of the Dons where Vito looks to stop the inter-family war and allow Michael to come home safely. Vito directs Tom to arrange the meeting of the Dons in NY, Chicago and the west coast in the scene before cutting back to Sicily. These arrangements, plus Sonny's funeral, would take several days to weeks to complete. The Dons have to clear time in their schedules, travel to NY, Bocchicchio hostages have to be delivered in their place. All of that takes time. Barzini would've had plenty of time to execute his plan in Sicily.

Barzini would've likely deduced beforehand that Vito called the meeting with a view to ending the war and bringing his son back home. Fredo wasn't suitable for the Donship, or Vito would've appointed him already. Sonny was dead (heh), so Barzini would conclude that Vito wanted Michael back with a view of making him the new Don. However, pre-emptively whacking Michael in Sicily would've been construed by Vito as an act of war and further treachery. Such an act could've provoked Vito to all out war. If Vito deduced at the meeting that Barzini was behind the treachery against himself and Sonny, he would likewise conclude the same if Michael turned up dead. Vito likely had that theory in mind before the meeting anyway. Hence his 'warning' at the meeting.

How does Barzini come out ahead? Simple: break Michael. He knows that he can't kill Michael outright, at least not yet. Michael has to come back to NY and take the Donship of the Corleone family. He can, however, break him inside and make him lose his spirit. Thus, the Corleones would be easy pickings. The way to do that: kill his love right in front of him. Apollonia was the real target all along. An infamia, to target one's innocent family, but would that really concern Barzini?

In Sicily at Tommasino's compound, Michael speaks to Fabrizzio and orders him to get the car. Fabrizzio makes the point of asking if Michael is driving himself and if his wife is going with him, to which Michael says that he wants Fabrizzio to take her to her father's house temporarily. Fabrizzio gets the car, which is likely kept in a garage and thus the perfect place to install the bomb. He couldn't do it in the open courtyard, lest he be caught.

Fabrizzio brings the car out to the courtyard, out in the open and a fair distance from the house. (Why didn't he park the car at the curb of the house instead of so far away?) Apollonia is most likely out in the courtyard already wandering the grounds when she sees the car come out. We know how fascinated she is with driving by now. At this point, Fabrizzio would cut the engine, arm the bomb and get out. Since Calo already knows that Apollonia is in the car waiting and Fabrizzio is just exiting the compound just as Michael comes down, Fabrizzio knows fully well that she's in the car. She probably got in the car as Fabrizzio was getting out.

The trouble is, Fabrizzio had orders from Michael to take Apollonia to her father's house himself. If the bomb was for Michael, why was she still in the car waiting for Michael? Why was she not at Fabrizzio's side on her way to her father's? She would've been the perfect alibi against suspicion when Michael was killed. The two of them could've been out of the compound and halfway to the Vitelli home when the car exploded. Instead, he was standing there, looking dopey and crazy eyed when Michael came down, only running out when Michael spotted Apollonia.

Why was he still there? I believe that he needed to see the car explode with Apollonia inside, see that Michael survived and was there to witness it. All of this to report to Barzini, who would then spirit him out of Sicily and set him up in his pizza shop later on. Certainly, Fabrizzio had ample opportunity beforehand to assassinate Michael if he wished; he was trusted to be alone with Michael whilst carrying a loaded lupara. Do the math.

In short, my overriding theory about this sequence is that Apollonia was the true target of the assassination in Sicily, not Michael. It was Barzini's attempt to break Michael so that he would lose his fighting spirit and make the Corleones easy pickings for his conquest after Vito's demise. The trouble for Barzini was that while he succeeded in breaking Michael's spirit, he also took away Michael's conscience. He helped shape Michael into the Don he would become...and by so doing, engineered his own demise.