I thnk it's important that you are comfortable in your own home, and it doesn't matter what other people would do, or whether they would be ok with it - it's your home, and your feelings are important.
Personally, I hate 'droppers in' with a passion, and it's almost worse when it is close family, as they are more likely to pick up on things than strangers would. My own mum would drop in when she lived closer, and would then read what was on the calendar on her way to the loo, and comment on appointments etc, as well as noticing all sorts of little things that are private in your own home.
My sister really doesn't mind people dropping by, and leaves her door open in case she doesn't hear them knock. I, on the other hand, keep the doors locked and quite often don't answer the door if I'm not expecting anyone. That doesn't mean that she cares more about our mum than I do - it's just different boundaries.
When you go back to work, it might get worse. I worked full time, and really valued downtime when I was a home, whether enjoying time with my husband or just watching TV in my pyjamas. I think that we all have every right to please ourselves at home, and that doesn't mean that everyone has a right to know about our private lives.
It's a tricky situation, as it is clear that you don't want to hurt your MIL, and it sounds as though you might have to be blunt with her - some people genuinely think that they are 'different' when it comes to things like this, and she probably really doesn't know that she is being a nuisance.
I agree that your husband would be the best one to have a word. He could present it as a 'you know the British' sort of thing, and he might pull it off. I do understand the 'nonna' thing, though - a friend of mine had the same problem when she married an Italian, and never really sorted it out, I'm afraid.
Good luck, whatever you do. I hope you find a way that allows you to enjoy your baby in the way you want to, and that your MIL learns to respect your boundaries, whether she understands your need for them or not.