Thanks so much everyone for taking the time to reply. Even if I can't reply to all of you, I have read every single one of your messages carefully, trying to understand the sentiment and arguments.
I hope more posters feel encouraged to share their perspective. I am finding it hard to discuss this with people in my social circle who have as much as an opinion on this topic (they don't have children or grandchildren), so trying to gauge what is reasonable and appropriate has been hard.
For those who asked, I am the DIL. PIL are nice people. But, as another poster already suggested, helping is often about their need to be useful rather than about making our lives easier.
Some of you might probably argue that I can't possibly know that—I do, because their offers to help are constant and if refused, (my MIL particularly) will either not say anything but look clearly disappointed or insist "but I want to do it/ I want the baby to have something from me". Then they bring it up again and again.
For example, they will offer to buy something functional for DC and we say we don't need anything, we've got it sorted thank you. Both PIL will then start listing the kinds of things they would be willing to buy (what about this? And that?). "No, thanks/ please let me check if we have one at home first." Then everytime we visit they keep bringing it up: "We'd like to buy this and that." We can have this same conversation with both PIL 10 times easily. It's draining.
My parents are very laid back on the contrary. I never thought I would feel smothered by someone offering their help to me—after all, it is a very kind gesture, right? Initially I was thrilled that they were so helpful all the time. But now I feel as if I'm expected to accept their proposal, otherwise I am perceived as hostile and it's not a nice feeling. In other words, they feel entitled to help/ participate, so "I can hold the baby while you eat" can only be met with the reply "OK, thank you", even if I want to hold my baby for whatever reason or simply don't want help.
In my opinion, if they really cared about being helpful, they would listen to us when we express our needs, and I would be more receptive to their help.
In addition to all this, it feels like their focus on us is very intense from the minute we arrive. They hover over us while interacting with the baby all the time, watching our every move and making remarks all along.