I’m a simple man, so I like to use the dictionary when there’s a disagreement about what something means. In this case, my phone’s dictionary, which cites the Oxford American dictionary as its source, has the definition of ‘nuclear family’ as “a couple and their dependent children, regarded as a basic social unit” and I’m not seeing how anything I wrote is in disagreement with that.
Sure, people often grow up with other relatives. But we have other terms for them, which belies their reduced importance in our lives vs our parents and siblings.