Quote
Originally posted by AppleOnYa:
In my opinion their relationship is already mended by the time the movie begins. In his letter we hear him reciting to his children at the opening, he mentions that their schooling had been managed by their mother. Also, Kay is a guest at the reception following his being honored by the church. They somewhat reasonably discuss their concern for lives & futures of their children. Far different attitude from the 15-20 years earlier when Michael didn't even want to see her face. They are no longer in love, but have already reconciled.Apple
I don't think they were on good terms at the beginning of III. Mainly because Kay was very bitter toward Michael and that they hadn't seen each other in 8 years. Kay talks about dreading Michael and how Michael's life was a sham. She scolded Michael, "This is greatness? You know Michael, now that you’re so respectable I think you’re more dangerous than you ever were. In fact, I preferred you when you were just a common Mafia hood."

Not until Michael agrees to let Anthony go pursue the musical career does Kay even act civil toward Michael.