Lollie, I subscribe.

Here's what I wrote on this subject, err, don't know how many months ago.

"The most important of all things that make GF3 plot absolutely unbelieveable is that Michael would NEVER give children to Kay. If something is impossible, that is. After all that we see and read, especially after the stare he gives her when he catches her visiting children, we must be convinced that he would never let her even approach them. That by killing his child she made him feel such pain, disappointment an even hatred, that it killed all his love and respect for her, whatever it could be, and killed forever. She could have no illusions about that, she wished to do it, she said “there would be no way Michael, no way you could ever forgive me.” And there is no way. Even if he didn’t kill her, that never means that he could forgive. And certainly, he is not an idiot to send his children to the only person in the world who would most surely teach them to hate him.
And of course, he would never say “I love you…Forgive me everything...” NEVER! And he would never complaint being feared. Anyone else could. Not he.
I think that he would rather marry again it would be more natural for him, and not only for the sake of his present children, but to have more. He could not be too desperate about losing Kay herself. And he was not the man to dream every night about losing her, and children he is supposed to have given up himself. He is not so sentimental and snotty, and there is a lack of logic in all this.
We know from the book, that he never loved Kay very much. Not even as much as she loved him. He easily forgot her for Appolonia, and then, when he returned home, would never resume their relationship if she didn’t seek it. She found him, came to him, he agreed to sleep with her and said something like, well, what about marrying me, if so? And when she asked him, why did he want to marry her, since he “obviously didn’t love her”, as she said few phrases before, he answered: “because I want you and I want a family. I want kids, it’s time”. In fact, then, having lost Apollonia, he would marry anyone who could give birth to his kids – just because if he was going to become the head of family, he had to have family and kids, the more the better. And kids were his strongest passion in life, remember him nagging Kay: “Does it feel like a boy”? He wanted sons, to help him in business, numerous sons, because he knew what business it was, and remembering Sonny, he knew if he had one son, anything could happen to him. And even if he had only two, the first of them might be killed, and the second might be Fredo…
Pain about the son she killed must have been much stronger than anything he could feel about losing herself. To that he was ready, as we know from the novel, she tried to part with him once, and Puzo gives us enough to show that their marriage could not last long after that lie of his, something most important, their mutual trust, was broken and they could never be what they were to each other. When in GF2 she comes to say that she wants to leave him, and does not feel any love for him at all, he is not surprised or grieved by it. He doesn’t give a damn about her feelings for him, he dismisses it as nothings. He says ”we'll have another child, and we'll go on.” He is not so much interested in her as a person, she is “His wife but not his partner in life”, as he said she would be, when he proposed her marriage. And wishing that child as he did, we can be sure that after losing it he would suffer much and would wish it still more.
And he is a normal man, and rather young, about forty. He can’t live like a monk; the novel describes him as a hot-blooded Italian male, who never refused making love, on the contrary, was quite devoted to the process.
Of course, being broken-hearted as he was, he would not perhaps feel a tremendous romantic love, but it will help him to chose rationally. And personally, I think his choice would be Sicilian. Having already kids with a half of fishy blood of “that washed out rag of an American girl”, he could not expect them to become real Sicilians, and we know from the novel, how difficult it was for Tom to be in the family business because of his not being a Sicilian, not having Sicilian cunning and subtleness. If he would marry a Sicilian, he would have at last truly HIS children, full works, who will understand and accept him, and will never prefer singing and law to the manly deed of family business. "