Kay did bring Michael's [two] children into this world!
I also think it's highly unlikely that there was an actual divorce or any kind of formal visitation agreement. Michael would never have allowed his personal affairs to be aired in court.
Sure thing Woltz “Michael would never have allowed his personal affairs to be aired in court†as Michael would “use all his power to keep something like that from happeningâ€
How did Kay get the kids? I doubt there would have been any divorce/child custody hearing [Kay didn't seem to have any visitation rights even] in Godfather 2 as Michael would “use all his power to keep something like that from happeningâ€
If Michael knew Kay was visiting the children, why was Connie desperately hurrying Kay to leave because Michael
was coming?
What more could Michael have done in front of the children and Connie “than close a door in Kay's face�
I believe whatever arrangements made, would have all been on Michael's terms
until Michael entrusted! the children's education to Kay
We are none the wiser when Kay got the children nor when Michael and Kay divorced All we know is -
How did Kay get the kids? When Godfather 3 came around / in between 2 and 3,
1. the children were with Kay
2. Michael and Kay had divorced