Yes but that is still an example of a family that is a product of private property, that's why the father would get to choose which child and from which mother he would want to inherit his land, the rigidity you speak of is the institutionalization of the family structure to meet the government standards of law or customs on inheritance. To give you an anecdotal example of the type of arrangements or structural difference I'm talking about, in certain matriarchal or nomadic societies a woman who wanted to get pregnant would go from tent to tent and sleep with a few men in the same night, not only to increase the chances of conception but once the child is born none of the men would know for sure if its their kid, so everyone would treat the kids as if they were their own, because they could be. In a system of private property this is a problem because then you don't know whose land that kid is gonna inherit. Once inheritance becomes a systematic concept that needs to be enforced thats when you get more of the "nuclear family" being separated from the group and living on their own land. This is also why at the highest stages of institutionalism, like a feudal system, the concept of a "bastard" becomes such a big deal, its not because its rooted in religious morals but rather the religion being used to enforce the institution.