Michael abused Kay’s love and trust many times. He even admitted, in his confession to Cardinal Lamberto, that “I betrayed my wife.” But Kay got back at Michael at least twice:

First, there was no way Kay could have known that her aborted fetus was a boy. Fetal ultrasounds and amneocentisis didn’t come into common use until the Seventies—and Kay had her abortion in 1958. She had the abortion because “this Sicilian thing must end,” and because there was a 50-50 chance her third child would be a boy. But, she told Michael, definitively, that it was a boy to make him feel the loss of another male heir to the Corleone crime empie—and to assert her own power over him.

Second, Kay tells Michael at the beginning of III: “Tony knows you had Fredo killed.” How did Tony know? He wasn’t in the boat with Fredo and Neri when Fredo was killed. He might have wondered why Uncle Fredo wasn’t around any longer, and have witnessed whatever investigation ensued. But the only way he could have known for sure was that Kay told him—to show him what an evil man his father was. Perhaps that was the reason for his obvious estrangement from Michael at the beginning of III.

TB, you're probably right about the abortion since Kay would have had it early in her pregnancy. Howevere, Tony would have found out about Fredo from any number of rumor sources just like Mary did (her conversation with Vinny.) Who knows where or how such rumors originate, but I don't think Kay was a source.

I could see her being the source. If he had heard it from someone else, he would have been much less likely to accept it at face value. Even if he had heard it from multiple sources, he could have discounted it as a common rumor.

Neither Neri, nor Rocco, nor Tom would have told him. He might have suspected it, but who'd confirm it? So, he might have said, "Mom, did Dad have Uncle Fredo killed?" All Kay had to do was nod.

Here's a better question: except for the principles involved, how did anyone know?

Exactly, how would Kay know for sure? She would have suspected, but would have had no proof.

Of course Kay wouldn't know for sure because she was barred from the compound. But it's reasonable to expect that Kay felt bitter, betrayed and resentful toward Michael. Plus, she knew what and who he was. So, when Anthony, naturally, started asking her about the split-up and other family questions, I can't imagine that Kay would have covered up for Michael. Sooner or later, he'd have asked about Uncle Fredo.

Come to think of it, I'm suprised Michael didn't have more children with other women after Kay. He could have easily had more sons if he really wanted to.

I think Michael's position would be that he got married once and that was forever. This would tie in with his public Catholicism, because he'd have to admit to some sort of mistake or failure to get an annulment to allow him to marry someone else. None of this would preclude a discrete girl on the side, of course.

Makes sense. Quite different post-divorce than post-death.