People don’t go every single week ( not saying it’s wrong if they do or don’t ) but yes they go every now and then. My sister in law got married and it was a tradition in her in laws for the DIL not to spend the night. There was a huge hullabaloo at such a thing and my MIL soon put a stop to this. Yes, it’s common in most places in Pakistan. I was raised in Pakistan. However, got married in the US, so never got to spend nights at my parents’ etc.
Anyways, in my opinion, if the husband and wife both are fine with the arrangement then the FIL shouldn’t be an issue. The FIL’s own wife lives in another country without him.