May I ask how old your baby is?
Y'know, I found that when my baby was a newborn and a lot younger (below 6-months-old) I tended to be more picky about how his grandparents (my mother-in-law--local Chinese lady) interacted with him. I tended to also get annoyed a lot more at their behavior. I think a big part of that was that I was adjusting to being a parent and I didn't want in any way to be undermined by my parents-in-law. I didn't want to appear incompetent and let them have too much reign in how my child was cared for.
There were also other factors at play--including my attempts to breastfeed, hormonal shifts after having a baby, health problems, baby not sleeping at night...etc. etc.
I find now, that I am able to relax a lot more and let some things slide with my parents-in-law.
I don't want to "take sides" with your MIL because obviously she is upsetting you. But, try to imagine things from her point of view.
If she is Chinese, she has basically been living her life waiting to have grandchildren. Also, Chinese grandparents culturally take a lot of responsibility for their grandkids--they are traditionally big influences in their grandkids' lives--and sometimes even "raise" the kids while the parents are working.
This is normal and expected (in their minds) and also is a huge honor for them--they love to go sit out in the park with their grandbabies and soak up the attention and adoration of others. They love to feel needed and like the wellbeing of that baby depends on them. Since their children have already grown up maybe they haven't felt like they were needed for some time. Especially grandparents who either did not work outside the home (housewives) or have been retired for some time.
They feel like being a grandparent is their reward for all the years they sacrificed while raising their own kids. My father-in-law once told me, "Having a grandson is so much better than having a son." What he meant was that now he can actually enjoy being in somewhat of a "parenting" role--whereas, when my husband (his own son) was growing up he was under so much pressure as a young man himself to work hard and provide a good life for his family (which in HK--especially in the past--was a crushing pressure) that he actually wasn't able to be that involved in my husband's life. Being involved in his grandson's life is sort of a redemption for him and has been good for our whole family.
Having said all this, I do understand that everyone needs boundaries. Boundaries are healthy and I think Chinese grandparents especially don't really understand how important these boundaries are. Culturally, they subconsciously think, "Because I'm older, automatically I'm right and people should listen to me and do what I say." So this can be very challenging because whether they understand it or not, you are ultimately your child's parent and are not obligated to hand over any authority for that child to anyone else. You DO have the final say when it comes to your child. I think your husband needs to understand that.
Now, how you communicate that to your MIL without hurting her feelings, making her lose face or completely confusing her, will have to be carefully planned. I do agree, that assigning her a task is a good idea to begin with. Instead of waiting for her to come knocking at your door, maybe you can be proactive. Call her up before she comes and say, "Oh, I just ran out of diapers, rice, baby soap etc. etc.....could you go by the store and get these things for me if you're coming over." Also inform her of your schedule. Tell her that you are putting your baby on a schedule and at a certain time everyone in the house is going down for a nap and it might be better if she leaves before then. Allow her time for visits but also lay down which days of the week you aren't accepting visitors (i.e. her). With your husband's willingness and help, all of this can be communicated clearly.
I hope you can work with your husband to set up some healthy boundaries that give you the space you need while honoring your MIL.
