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.