No, that’s baggage that people are bringing to the conversation. It merely means a couple and their dependent children. Whether or not they live separately from extended family has no bearing on the term.

I had to make an account for this but it's been incredibly frustrating seeing you going up and down this thread and dismissing interesting and well informed discussion with actual sociological background behind it based on a misunderstanding of terminology. I have never thought about the nuclear family for more than 5 minutes but it's clear to me that both uses of the term (in the way you are choosing to interpret it and in the broader sense that everyone else has discussed so far) are widely accepted in English. I would urge you to reflect in the future on why, when multiple people on a message board with seemingly well informed opinions and no obvious malicious intent try to persuade you that a term you are using has multiple definitions and connotations, you might choose to plant your feet on the ground and resort to a dictionary definition (not really well known for their completeness or depth)! If you had chosen instead to look up this definition in an encyclopedia, you might have found saving yourself (and me) a lot of angry typing. I hope you can find some humility and learn from this