I think that it would be inconvenient for Michael to have the kids around as they gained in undersranding. His business associates would arouse their suspicion.
Pete, your viewpoint gains strength from something Kay told Michael in III: "Tony knows you had Fredo killed." (Of course, Kay might have told him, out of vindictiveness toward Michael and to mitigate her abortion when Tony got old enough to understand it.)
As was pointed out above, Michael probably wanted his children educated away from Nevada. I'll guess that started with some sort of prep school. Also, Michael always wanted a veneer of normalcy, and once it sunk in to the community that Kay was gone he'd start to realize that it looked odd for his kids to be motherless in town, but escorted around by his cronies. Even his divorce would have to be choreographed for appearances.
Yes, he certainly would have looked toward his reputation as a "legitimate" citizen. Divorces still carried a hint of scandal among prominent people in the late Fifties and early Sixties.
