Great topic!
I think that Vito in that age was in the reflecting sort of life phase, and tried to figure whether or not Mike would get through it then with things were changing.
I believe that he had no doubt at all for Mike, he was the smartest and tactical son afterall. Vito just wanted to make sure. He was sure of Mike getting alright handling the crime family.
As for the natural family, I think Vito was worried more, because Kay was not an Italian and would never accepted this "Sicilian thing" ... Kay would never want to handle the family in their traditional way.