I've never been able to fully comprehend Michael's behavior in these scenes.

At first glance, it seems clear that the assassination attempt in the hospital leads to his decision to join the family.

However, his previous conversation with Kay had a real finality to it. There was no reason to believe that Kay (or Michael) were in danger ("Sollozzo knows he's a civilian."). As for protecting Kay's reputation, Michael was already known to be a war hero and estranged from his father's affairs ("Kid's clean, Captain. He's a war hero."), so that isn't a compelling reason to send Kay back to New England. And if it was the reason, I'd expect Michael to reassure Kay that he'd see her when things settled down a bit.

Instead, he basically dismisses her and tells her "don't call me, I'll call you." This behavior is consistent with Michael already deciding to be "with" his father, and being unsure how (or whether) Kay would fit into his life's new direction.

The question that remains is why did Michael do an about-face. There's no clear answer. I remain unconvinced that he was dissatisfied with Sonny's leadership.

Perhaps it was simply time for Michael to fulfill what Puzo would call his "one destiny."