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.
At the beginning of III, Kay shows up at Michael's Church ceremony with her husband, Douglas. I doubt she was a bigamist.
Now, this is a quandary.
I agree with Woltz that Michael would not want the exposure of his underbelly that would be the product of a divorce. On the other hand, as TB states, Kay was not a bigamist. So, what transpired?
Well, maybe Michael made a deal with Kay about a quiet divorce that would not expose his underbelly and her abortion: You give me the kids and I won't ruin your life. On the other hand, Michael's underbelly was already exposed by the Senate hearings. However, Michael would have been cautioned by legal counsel that once ya'll are divorced, your marital privilege (regarding testimony) disappears. Maybe he followed that advice until he made the decision to entrust the kids education to Kay. Of course, we don't know when that would have taken place: grade -school, high-school, college?
There are so many mitigating factors to consider here.
Good points, TB and Oli.
You're right, they got divorced at some point. But there's no way Michael would have allowed a contentious divorce proceeding in open court. Kay probably leveraged that to get control of the kids' education.
After 1970, no-fault divorce was available in parts of the US. That would have allowed Kay and Michael to simply state something anodyne ("We have irreconcilable differences.") and prove they no longer lived together to get the divorce. No court testimony needed.
So I'll assume they remained legally married until the early 1970s and then divorced on paper. That would have given Kay plenty of time to re-marry before the events of GFIII in 1979.
