I'm pretty sure that Michael had his marriage annulled. In GFIII, he really wanted that image of respect towards the church -- I think it was actually quite important to him that he succeeded that.

I think a good question is why should he remarry? During GFII, he is a husband that barely spends time with his family and is busy with his "business" all the time, so why should he have a pressure of a wife plus the pressure of his family business? I think he has abandoned all hopes for a third marriage because I think he really thought that he was a failure as a husband by the third film. He tells Kay, "I had a very different destiny planned for us."

And by the end of the second film, I think he felt little love for Kay. Her abortion really hurt him and his values. I don't think he can trust another woman again and he would most likely feel insecure in a marriage. I think marriage would consider a little "risque" for him.

As for what was shown in GFIII, that's still in question. I think spending time with Kay is sort of an escape for him. He has been spending the last few years with hopes for peace but he is always surrounded by those he do business with or the family members he have left. The goal of Michael in GFIII is to make the family business legitimite -- but wasn't that his goal all along? Kay is a bitter reminder of a promise he has yet to fulfill. Time heals and I think in the Michael and Kay relationship, it really did and Michael may have restored his love for her as time went by and he has grown into a old and lonely man. Family is his foundation and that is what makes Kay important to him. She is still the mother of his children, after all.

I might want to add that Michael is actually quite a controlling husband to what was shown in GFII. I can't blame him especially when bullets can sometimes well, fly through the bedrooms. Being the level-headed person he is, I don't think he would want to bring another woman in his deep underworld.

But that's just my "theories"