I have posted elsewhere my opinion that Connie is one of the great characters of the trilogy because she transforms from a rather innocent "spoiled guinea brat" to a slutty embarassment to the family, to Michael's caretaker, and finally as kingmaker to Michael's succesor, who in the process of promoting Vincent, makes her bones by killing Altobello.
The relationship between Connie and Michael is unlike any other relationship Michael has with anyone else. Perhaps because she is his older sister she is better able to identify and resist Michael's manipulations, and because of his guilt over killing her husband and later on their brother he doesn't try too hard to manipulate her. In fact no one gets away with more vis-a-vis Michael than Connie. She embarasses him with Merle and her other escapades, while he is bailing out her son from apetty theft. When she re-gains her senses she returns to Michael, tells him he needs her, and right away she is back in the family acting as Michael's caretaker, and eventually confidante. The first thing she does once she is ensconced in the Tahoe home is sneak Kay in to see the kids, completely against Michael's orders. When Michael catches Kay in the house his wrath is directed to Kay, not Connie, and we do not see where Connie pays the price. Eventually, as we know, Michael sends the kids who he swore Kay would never "take" back East to her ostensibly for their educational benefits.
Connie had to have had a role in this decision. Then in III after she "gives the order" to hit Zasa, Michael rebukes her, but does nothing to diminish her influence. Instead, her influence over him increases, and she becomes a power center in the family. Contemplating Michael's possible assassination she asks Vincent in the pool room scene if he has arranged everything if the worst happens, and she tells him he is the heir apparent because he is the only one who has Vito's strength. In fact it utrns out IMHO she also had Vito's strength and Michael recognized that in her, and used it for the good of the family despite the fact that she never really marched in lock step with him. It is a relationship unlike any other Michael has.