Michale's drive, throughout the three films, is to make the family legitimate. By this point in Part III it has become obvious that, in so far as the " family " is concerned, he cannot achieve this. The Corleone " family " must remain mired in death, intimidation and voilence.

I believe that Michael shifts emphasis - if he cannot keep the " family " clean he can at least keep his own, personal family out of it.

He does not include Vincent in this family, nor does he want to since Vincent embraces the very life Michael rejects and possibly also because Vincent is an illegitimate off-shoot of his personal family. So, he wants Mary to have nothing to do with the Corleone " family " at all - she is titular and probably eventual real head of the legitimate business - and she cannot, will not, be involved in it through marriage to Vincent.

So, I believe it was your first theory that motivated Michael, Don Cardi - if he could not save the " family " he would at least save his family. Most intriguingly, this is the very reversal of the decision he makes at the end of Part II.

Warmest regards

dave