Remember that one of the main reasons that Michael was attracted to Kay was that she represented everything he hoped to attain: that WASPy legitimacy that he craved. She was everything that the Corleones were not.

If Michael, in his endless quest for that legitimacy and societal acceptance, wanted that for his children, what better place to get it than to grow up under their mother's influence? She would provide them with contacts within the legitimate world, either through their education or her friends.

That truly is what Michael wanted for his children, and I think that he finally recognized that it was not something he could provide, but that which was only accessible for them through Kay.