A nitpick that has caused much confusion in the comments below:
The nuclear family is the most basic form of family, and is certainly not opposed to an extended family. An extended family is a superset of a nuclear family. All families by definition must include the subset of the nuclear family, and thus it is the minimum requirement to fall into the set of "All possible families".
For the set of all families F, there exists an element N = "nuclear family" such that N is a subset of F.
This is not true. If the children don't live with the parents, it's not a nuclear family. If one parent is dead or the parents don't live together, it's not a nuclear family.
If dad's abusive and mum can't cope, and the grandparents are taking care of the kids at their place, it's not a nuclear family - the supposed 'nucleus' is not there.
If there are no children, but adult siblings live together, they are a family, but not a nuclear one.
My old boss took in a couple of teenagers from up the road when their mother was caught cheating and fled, never to be seen again, and the father was a pilot, always away, and utterly useless with kids. So here you have a situation where there is a sort of stepmother (no formal adoption) taking care of two kids (who come to see her as mum), a separate father who's not really in their lives, and a biological mother who has never been seen since. It's hard to see how terming that fractured family as a 'nuclear family' allows the phrase to have any useful meaning whatsoever.
You are speaking of time variance. At some point in time, by definition, the nuclear family was present. It takes a male and a female to produce an embryo. At this point, the nuclear family is created. What happens afterwards is of course a combination of choice and probability, as your plethora of examples indicate.
The only thing that is important in my assertion is whether the nuclear family unit is purposefully maintained by the parents, or not. The many reasons outside of the parents' control which may contribute to its dissolution are not part of this discussion (accidental death, dislocation, disease, etc.).
As with any problem, we must be careful in defining our variables and assumptions, and minimize both in order to reduce the complexity of the problem, but not so much that the problem being solved becomes trivial.
That does not mean that all families are supersets of a nuclear family. A stepfamily years down the track is not a superset of an earlier nuclear family. It's like saying that the cars on our roads are supersets of aluminium ore, there just happens to be time variance. Or that synthetic clothing is actually made from trees (via swamps -> oil) and therefore a superset of natural clothing, there just happens to be time variance.
And, strictly speaking, an embryo is not always created at the time of intercourse. Even if your definition was correct, it is possible for the father and mother to be together, the father to leave, and then for the egg and sperm to meet. This can be be up to 3 to 5 days later.
Your definition of family has become so vague as to be meaningless. In genetics, adoptive parents are not considered family. I recommend you look into the evolutionary foundations of human mating systems, and their consequences (e.g. kin selection).
When did we specify we were solely talking about genetics? Do you really declare that the stepfamily down the road isn't actually a family? That's just nonsense from a political, social, or philosophical standpoint, and doubly so when you consider that the term we're using - nuclear family - is most often used in these contexts. I'm a biologist by training (though not a geneticist) and I've never seen the term 'nuclear family' used when talking genetics, but I've seen it a great many times in political and social commentary.
In any case, what society considers a family has more impact on how humans treat each other than what genetics considers a family, so I don't see how you can so casually discard non-genetic definitions. If you go to a court that deals in family law, they certainly don't limit their definition of family to pure genetic strains.
In principle, the father could have died before the embryo was created - either during the time between intercourse and conception, or further decoupled with sperm banks &c.
I didn't mean "opposed to" in the sense that "extended family" excluded the nuclear family (if present) but just "opposed to" in that they are not the same concept. That said, as vacri suggests, it's possible for there to be family that does not have a nuclear subset (orphaned children live with grandparents, or what have you).
The nuclear family is the most basic form of family, and is certainly not opposed to an extended family. An extended family is a superset of a nuclear family. All families by definition must include the subset of the nuclear family, and thus it is the minimum requirement to fall into the set of "All possible families".
For the set of all families F, there exists an element N = "nuclear family" such that N is a subset of F.