Both Connie and Vito's wife have complained to Vito about Carlo's abuse of Connie and urged some sort of intervention. Vito has refused to do this, mostly because he believes in staying out of marital disputes as well as thinking every man is a king in his own home. Even knowing that his only daughter is getting the stuffing beaten out of her on a regular basis Vito refuses to use the considerable resources at his disposal to "convince" Carlo to stop. So staying out of domestic disputes is apparently a pretty important goal for Vito.

Vito ordered Sonny not to intervene. Vito was apparently pretty po'd that Sonny did intervene.

"But the Tattaglia Family had not streamlined itself for the war, [the news about Sonny’s appearance and assault of Carlo]still had to go all the way through the insulation layers before [it] finally got to the caporegime who contacted the Tattaglia chief. By that time Sonny Corleone was safely back in the mall, in his father’s house, in Long Beach , about to face his father’s wrath.”

Angry about his public humiliation, Carlo either approaches or is approached by the Barzinis--goodbye Sonny.

But what if Carlo had gone to the mall to complain in person to Vito? How would Vito have handled it? Was there a way Vito could have finessed this situation that would have (1) Given Carlo some sense of justice (2) Stopped the beatings (3) Prevented Sonny from reacting violently again (4) Allowed Vito to maintain his non-interference policy.

My guess is that he'd tell Carlo about what he told Connie: that Carlo should learn to act in a way that didn't infuriate Sonny. Vito could rebuke Sonny after the fact, but he couldn't watch Sonny 24 hours a day.

Yup. That makes sense.
Perhaps Vito would “listen rudely” to Carlo and then say something like “I don’t interfere in other men’s private affairs. But if you beat my daughter I can’t help you with Santino. We won’t discuss this again. Now please leave. It’s late and I want to see my grandchildren before I go to bed.”

Yes, Vito's attitude was not to interfere. But, if Carlo had complained to him about Sonny, he probably would have said, "What goes on between you and your wife is none of my business. Now you've made it my business by complaining to me." He would have lectured him about being a real man, along the lines he lectured Johnny Fontaine, except more forcefully. I think he would have been much harsher with Sonny--not only for interfering between a man and his wife, but also by exposing his temper--his main weakness--in public, which Vito would have known would lead to a bad end.

You're probably right TB. However, Vito's indifference to Connie's suffering is one of the most disturbing parts of the novel. Equally disturbing was Vito's apparent admission that he would have beaten his wife if she had given him reason to.

In a way, it's not surprising. Afterall, he was willing to drag his sons into his murderous way of life.