I would try and set a pattern and timetable for when she can visit, I deduce she lives close by, and if she comes outside these hours, then do not answer the door.
I would contact the massed family and say to them how happy you are that they love your son, but too many visitors too often are making it difficult to set up proper routines and, in this COVID age, you are conscious of the infection dangers to a small baby from too many people holding him and breathing on him. Perhaps, if he has a day when he seems a little bit unwell, or is teething, you could hurriedly cancel all visitors for a day or two because of the fear of infection. You can say that visiting is by pre-arranged visits only.
When your MiL is with you. Ignore her when she does something you do not want, take your baby and go for a walk alone or retreat to your bedroom with him and shut and lock the door to keep her out. if she acts sensibly, shower praise on her. It is what we do with children. Why shouldn't it work with adults.
You have a highly admirable partner. Standing up constantly to his own mother cannot be easy. Imagine yourself in his place in relation to your own mother, constantly having to admonish her and tell her to back off, so lavish praise on him, saying how well he is doing in such a difficult situation.
You are in a really difficult position, but seem to be handling it incredibly well. keep us posted.