Maybe so!

“The Pope...the Holy Father himself…. has this very day blessed Michael Corleone and you think you know better than the Pope?!!”

pulling your leg! aside,
I reckon, Michael was pretty much “very publicly linked to organized crime" and 'looked' guilty” in the “court of public opinion” long before the senate hearing, out of which, Michael “got off” in my opinion, 'looking' better than before the hearing!

1. all of the below and some! were “put in the record” by the senate chairman
2. Michael having never been arrested or indicted for any crime whatsoever
3. Michael issuing a challenge to the senate committee to produce any witness or evidence against or
4. to clear Michael's name with the same publicity with which they have now besmirched it

Exactly! Woltz
If Kay had concerns about how the existing son 'not' fine Anthony is turning out, in my opinion, as a mother, Kay could [should] have stayed on and nurtured her children as best as she could, not leave them behind in Michael's way of life especially during their most formative, helpless, impressionable, vulnerable years

Ref: How did Kay get the kids? [Thanks Turnbull for the link]
Wow! so many threads! There isn't enough time!

Whilst it is somewhat unclear, exactly how long [perhaps up to University age?] Anthony and Mary were with Michael, looking at them in Godfather III they seem to have turned out pretty good and I believe credit should be given to both the parents

Anthony and Mary's foundation would have been laid, when they were with Michael?
Also Kay tells Michael “Only if you let Tony go free, to have his own life. Away from you” Does this mean Michael was still somehow involved in their children's lives?

It seems, Michael's way of life was finishing! or trying to finish!! [Immobiliare?] by Godfather III [it never ends!]
And Michael did end up remorseful for his sins

Michael still had the drawing Anthony left for him on his pillow, all those years ago
Anthony said to Michael, he will always be Michael's son but will never have anything to do with the business. Fair enough!

If my memory serves me right,
As regards Mary, Michael surrounded by his family, was parading himself and his family in public, so out in the open even at the steps of the Opera house in Sicily, in the night, in full view of anyone lurking knowing Mosca, the assassin who had never failed thus far, was contracted to murder him and that Mosca had already murdered Don Tommasino Go figure!