I think it's great you are trying hard to learn and be accommodating. I'm Chinese in a Chinese marriage, but even so the culture is very different at my ILs (they are more religious and traditional) so it was a bit daunting for me because I don't know what are the landmines and my hubs doesn't know where the knowledge gaps are.
I think you shouldn't overthink the cultural divide and their "seniority". As with any relationship where you are "the new junior", most importantly is to make them like you. Pay compliments, bring thoughtful gifts, offer to help, be cheerful, listen respectfully even when you disagree. The older folks tend to be really bad with words and thoughtless so just take everything in stride with a big pinch of salt. As long as your husband is supportive of you it's fine!
It's quite... 1900s to be thinking you "own" your DIL, so I think it may just be poor choice of words. The common gripes I hear from people 50 to 70s is that it's better to have a daughter coz the daughter will care about you and visit you while the son is aloof. So yeah, generally the DIL still hangs quite a bit with her family, as long as both you and your husband are comfortable that arrangements are fair.
Lastly I think there are nosey and opinionated families in every culture lol. Peaceful life with others will always be full of compromises, have your husband help draw the line, fake ignorance and make your decision anyway, or let some go and pick the battles you want to win. It's your husband,kid and your life that matters most at the end of the day, it's good to keep ILs happy but don't stress too much over it. All the best!