When did we see anyone asking Vito's blessing in marriage? If anything, the flashback scene at the end of GFII seems to indicate that Sonny gave his blessing to Connie and Carlo's marriage--Vito obviously had no respect for Carlo ("...never discuss the family business in front of him"). And we don't see or hear of Michael asking Vito's permission to marry Apollonia. Also, Vito's only sibling, Paolo, was killed before Vito came to America.

4. When Michael greets Sonny’s now older, football-playing son, he says, “Santinnoooo” – like his father in another edited scene, who greets his son with a similarly long pronunciation of the name Santino.[/QUOTE]

This tiny but very important interchange was cut out of the Gardiner Shaw scene on the DVD "extras" disc. Too bad, because it gives us a clue to the age of Sonny's kids. [BTW: how do you know he plays football? Did I miss something?]
Probably it was cut to save time. I don't disagree that it shows a "warmer" side to Michael, MC--particularly when he said he'd been like a father to Francesca. But I also detected more than a hint of calculation and manipulation in his tone to Gardiner--he gives him that cold, Michael Corleone gaze and asks how he intends to support his bride on a fine arts degree. That's something that an ultra-WASP (like Gardiner) would ask an Italian guy who wanted to marry his daughter. Michael's also plenty calculating when he tells Tom, "Make sure her dowry's big: these people believe Italian brides go barefoot."
(Note to MP and MC: I agree that this--and all the deleted scenes--should have been included. Every one of them is worth watching and adds something to our understanding, especially the Gardiner Shaw scene and the Genco deathbed scene. That's why the TV "Saga" version is the best one.)