I dont think that Mary is part of the assassination. Once Michael is out the way Mary is at the helm, who would turn to Vincent to (help) run the company. Altobello/Luccesi believe that they have Vincent, and so believe that they run the company.

I also agree that GF3 lacks the strong plot that the other 2 have. I am a strong believer that if they did have Robert Duvall then the film would have been much better, and that there would have been a better story line involved to give it that ingredient the other 2 had.