There isn't anything inherently wrong with one man and one woman living in a monogamous relationship and raising kids together.
The important thing is establishing that such an arrangement isn't the one, true, glorious way to do things, with the corollary that children are not the property of the people that make them.
If we're talking about a society at an appreciable degree of socialist development where private property is effectively abolished then children shouldn't be considered the property of their parents, either. Childrearing should be a common, communal process where a child's development isn't placed at the mercy of only two people.
This isn't necessarily to say that they should be torn from their parents and put through some sort of agoge-esque program, but that children become the responsibility of all functional adults. How this will be expressed will of course differ from community to community, but it would be both a natural and necessary development in the shift from the competitive mode of production of capitalism to the cooperative mode of socialism.
In any event, every adult effectively becomes the parent of any child. If another adult witnesses abuse against a child (by which I mean for the sake of this example severe physical harm, psychological mistreatment, starvation, sexual abuse, or other such mistreatment, as opposed to a simple spanking or sharp word), that adult should be empowered to immediately remove the child from the guardianship of whoever is currently "in possession," if you'll excuse the phrase, of the child.
Ideally this would be a temporary situation contingent on finding long term care for the child and remedying, if possible, whatever caused this maltreatment in the first place. I would hope that under a socialist paradigm such incidents would occur more infrequently, but I don't doubt that under socialism there will still be people with mental disorders (narcissism), unhealthy sexual proclivities (pedophilia), etc.
From there I think it would be up to the community to decide whether the offending adult is sanctioned or provided rehabilitation or imprisoned or permanently separated from the child or whatever, depending on the circumstances and severity of the abuse.
So what? People used to divine the intentions of the gods by cutting a person open, nailing their intestines to a tree, and then making them crawl around it until they died. We (generally) don't do that any more, either.
During capitalism the state has taken over the heavy lifting of raising kids by forcing them through regimented, production-line education. That's been going on for a while too, so should we just keep doing it?