In a deleted scene after Connie's wedding, as Michael and Vito are waiting for the car to take them to Genco's deathbed, Vito says, "Did your American girlfriend get home alright?" Inferred serious disapproval.
And the Don was right in his disapproval. Vito knew that an old school Italian wife would never disapprove, at least openly, of having a husband who would live that kind of life. Mama Corleone never questioned Vito about his business. Appolonia never questioned Michael about his business. American Kay was nothing more than a continuing thorn in Michael's side as far as the family business went.
Bottom line....Kay thought that she could change Michael and at the same time Michael thought that he could change her. Both were fooling themselves.
