Ref: How did Kay get the kids? [Thanks Turnbull for the link]
Wow! so many threads! There isn't enough time!

I still doubt there would have been any divorce/child custody hearing [Kay didn't seem to have any visitation rights even] in Godfather 2

I concede the children “did end up with Kay eventually” as we found out in Godfather 3

However...
We are none the wiser when Kay got the children....“We don't know when the epiphany started”