"... the more I reflect on Michael's character, the more I realize how tragic his fate was."
Absolutely, Lavinia. I always thought that Part II played like a perfect Shakespearean tragedy, with the protagonist's nobler intentions struggling with and ultimately losing out to his darker ambitions. By the time Part III comes around and Michael finally builds a closer bond with his daughter Mary, he loses her too -- another cruel irony imposed on his tragic life, as Don Cardi noted.
And how true that parents also want to build a better life for their children than the one they had. As you observed, Lavinia, Michael didn't get the chance to be a judge, a senator, a diplomat ... it's very well likely that he wanted Anthony to have that chance. But by focusing so intently on protecting the family business -- the power base that would open all the best opportunities for Anthony -- he lost sight of the fact that there is and would be more to Anthony's life than the way he would make his living.
I had forgotten Vito's line until Harry brought it up -- that "a man who doesn't spend time with his family can never be a real man." I bet those words were circulating in Michael's mind as he stared at the little red car abandoned in the snow.