When Sonny was murdered and they knew Carlo played a hand in that, how is it possible to keep Carlo alive for that long?

How many years has passed before they decided on The Massacre?

This is why reading the novel is so helpful. In it, Vito states that he just doesn't have what it take anymore to do what's necessary. Michael kept Carlo alive in order to use him as a component of his overall plan.

Yes. As Vito said at one point, Sonny's death left him "short of sons." His number-one priority was to bring Michael back, not to whack Carlo. And he didn't need to have to deal with Connie's grief if he had. As Oli implied, keeping Carlo alive was a way to signal Barzini and the others that he was "weak," and didn't know who was complicit in Sonny's murder, or didn't have the coglioni to whack his brother in law, That would relax them and make them too confident--just what he wanted.

A part of Vito probably didn't want to kill the husband of his daughter and the father of his grandchildren. Once Michael took over, he announced Carlo was going to be his number one man in Vegas -- which was a ruse, and after Vito died Michael did what he had to do. After all Carlo's newest baby had a Godfather!

Vito knew what Carlo was, that he beat his daughter, that he was not a good husband. He knew that before the wedding, even. But it was his daughter's choice, she loved him (or perhaps believed herself incapable of being loved by anyone else), she had children with him. He couldn't bring himself to murder a member of his own family, no matter how deserving.

Yes, Vito knew that Carlo needed to be killed, but as has been said, his priority was to make the peace and bring Michael home safely, especially after Sonny and Apollonia were murdered. And he couldn't break his word. He passed that onto Michael, to do what he couldn't once he was gone.

What's interesting is that the book states that Carlo became a "model husband" once he was given more responsibility within the family.

In the film, I think a certain credit needs to be given to Gianni Russo. He does a great job of conveying the arrogance that went with Carlo's character.

Plus Vito was firmly against invading the institute of marriage, one of my favorite parts in the book is when Connie is complaining about Carlo hitting her and says Papa you never hit Ma(not me opps), to which he replies "she never gave me a reason to hit her."

Yes, that passage confirms Vito as a thug, a malcreant. The apposite of that passage is that had he determined that he had a reason to hit her he would have. But such reasoning by Vito is characteristic of his approach to life: do what I say or I will hurt or kill you.