To get back to the original question: I think that by GFIII, Connie wanted to both ease out Michael and make Vincent his successor. She saw Michael getting old, frail, trying hard to legitimize himself--and still having connections to the old ways, no matter what. I think she genuinely loved her brother, and I don't think she was trying to "get" him for Fredo's death. Connie may well have been in denial about Fredo's death, but by GFIII, I think she was over it.
She saw that Vincent defintely had leadership qualities, but needed exposure to Michael to gain patience and perspective. So, she cultivated Vincent and maneuvered him into Michael's orbit.
Don't overlook Vincent's own manipulativeness. Connie may have inveigled him an invite to Michael's party, but he makes a great flatterer's entrance: "How's my favorite aunt?" Connie bucks him up in Michael's presence by complaining that Zasa is ruining the old neighborhood. But then Michael takes Zasa's side! He tells Vincent that he was "foolish" to turn down the position Michael had offered him previously, and then Zasa took him in "out of the goodness of his heart(!)" He then tells Zasa he has no quarrel with him, and orders Vincent to "make your peace with Mr. Joe Zasa." Had Vincent done it, he'd have been shown up as a wuss--and Zasa would have taken it as carte blanche to whack Vincent. Instead, Vincent lays down the classic Sicilian challenge--biting Zasa's ear--which forces Michael to put family ties ahead of his (shaky) peace with Zasa.
Another (admittedly remote) possibility: Michael took Zasa's side to test Vincent and see if he had real coglioni.