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 happening”

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”

Sure thing “Kay [mother of his children] was the one person Michael couldn't [wouldn't] kill”

In my view,

As soon as Kay revealed she had an abortion, irrespective of this Sicilian thing, unholy and evil everything must all end, Kay had already lost the case!

If the Senate committee “what the hell happened here!” couldn't pin anything on Michael when they had -
1. incredibly clever and resourceful Roth
2. Senate lawyer Questadt who belongs to Roth
3. Turncoat Senator Geary
4. Willie Cicci
5. Frankie Pentangeli

chances of 'vindictive' 'lying' 'murderous' ex-wife, out to destroy, Navy Cross war hero 'law abiding' patriot, in bitter divorce process, is buckley's and none!