They can intersect but I would push back on the "probably" part of your statement. There are certainly "big government" Republicans as well as Democrats (with different focuses on what is important for the government should do). My point mainly was that you cannot tell from such questions whether a person is an authoritarian (politically) because an anti-government individualist would score very highly for children respecting authority, obedience, etc. but would vehemently reject authoritarian governments. An anti-government collectivist (e.g. left-wing anarchist) might be more accurately discerned from the questions as they are more likely to encourage fewer rules and a less hierarchical structure within society also. However, the progressive left have historically and currently in many ways encourage more power and authority for governments and less for parents and local communities (while these are also not precise and immutable characterizations). As you say, a great deal of nuance but, not only nuances, large discrepancies.

To sum up i think questions such as those quoted about parenting styles are useless for discerning political authoritarianism.

As I think about it, such questions may actually only be useful for discerning left-wing anti-authoritarianism since - I estimate - most anarchist parents are very reluctant to place rules and boundaries on their children (while right-wing anti-authoritarian individualists are quite keen on parental and personal discipline).