This is a really good question! I’ll do my best to try to help you out.
そういう is definitely an interesting expression. In my experience it tends to provide emphasis on the things it’s pointing out. Let’s try breaking down the original example you gave: 千尋さんそういう面倒くさい部分.
Your intuition on the sentence is actually really good and it’s totally understandable why you might thing the husband might be referring to the annoying part of their conversation. Of course, one way your tutor may have come to their translation is by understanding the context better. However, if I were to read that sentence I’d also assume that the speaker is referring to Chihiro and not something outside of the context.
I said earlier that そういう provides emphasis. So then, why do would I assume the emphasis is on Chihiro and not previous parts of the conversation? This is because そういう is typically used to describe something while providing emphasis on that item and the applied characteristic. You use そういう to emphasize that you are directly applying a desired or perceived characteristic to something. Chihiro is directly referred to in the sentence, but what annoying thing she might have said is not.
All that being said it’s not entirely out of the possibility that the husband was referring to something annoying Chihiro said, since そういう can also be used in that manner. The bit you provide is kind of an incomplete sentence so it’s difficult to tell?
What does make things a little bit more complicated is that there’s also the phrase そういう事 which can be used without referring directly to something, because it’s often used as a response to indicate agreement.
