They are often correlated and found in similar cultural sources, but they are distinct elements. The US idealization of the nuclear rather than extended family and corresponding weaker family ties didn't (and still often doesn't) come with the breaking of patriarchy -- in fact, it is rooted in a time when patriarchy was quite strong -- though you sometimes (especially now) find non-patriarchal arrangements along with it.

Strong family ties and non-transactional view of family interactions doesn't have any essential tie to patriarchy, nor do weak family ties and a transaction approach to interactions have any essential tie to the absence of patriarchy.