Though I don't like Duggu's character on whole but in this situation I find only his reaction realistic.
Akshara trust Naitik and that is good. It goes by her nature too. As a good wife and mother she is advicing Duggu to keep himself out of it. But Duggu is not the kid anymore, he is an adult and about to get married. He is old enough to understand his mom's pain, tension and fear as well as his Dad's lie, hidding secret and fear.
I don't think he should just stand like statue when he knows there is something a miss with Naitik's behaviour in HongKong as well as in India post HongKong trip. Naitik is giving every reason to doubt on him. His ignorance towards Akshara and Kids in HongKong is so out of character for Naitik as a person. Anyone in Duggu's place would doubt Naitik if he had witnessed and felt those things. Also the fact that Duggu knows Naitik didn't went to HongKong on work purpose and Naitik is lieing every damn occasions when questioned.
Why would Naira question? She is a kid who don't understand these adult talks or hidden secrets.
Questioning your parents does not equate to disrespecting them if done in right way. Duggu's way of speaking can be questioned? But the notion that he should not question his parents is wrong in my opinion.
Duggu/Naira has every right to question and demand an answer from their parents if they think that any one of them is hurting other.