I think once Sonny was killed, Sonny's wife took the kids away from the family business and sheltered the kids from that way of life -- the same way of life that killed Sonny.
Connie had kids, yes, and that would have been interesting to see one of them come through the ranks like Vincent did and see Connie pulling strings behind Mike's back... but part of me believes that Connie lobbied for Vincent to keep her own kids out of the family business as well.
Connie knows better than anyone what the family business can do to a person so why would she want to subject her kids to it? Sure she loved Vincent because it was a way to connect with Sonny -- who's death she still felt responsible for -- but Vincent was also somewhat detached from the family in the first place, so it was easier for Connie to get behind him when it came to the family business.
I do agree that the Vincent character comes out of nowhere (although the Lucy Mancini connection was cool) and it's such an obvious dues ex machina, but I think that as the film plays out, Vincent's character works, like many things in the film -- even though it is still flawed.
And I'll agree with the dialogue. A lot of it is eye-rolling inducive.