I don't agree that everyone wants a polyamorous and open relationship. Myself, I am in one, and it suits me.
However, how do you define a family? Polyamorous families exist, families with parents in open relationships exist, and they are just as much families as monogamous families.
The common definition of a family, and the one referred to by the article is "a group consisting of two parents and their children living together as a unit."
OK, but what of the other families I mentioned? Are you simply saying they're not families? Neither does the definition mention the monogamy of the parents.
They're not families according to the usual definition, and I don't see how two parents could live with their children together as a unit without them being monogamous.
What you suggest seems to go again the Universal Declaration of Human rights (Article 16.3) which states that:
"The family is the natural and fundamental group unit of society and is entitled to protection by society and the State."