Ok wow. I was all set to think you were being controlling but this description has my stomach in knots & I don’t even have or ever want children myself !
First off is your husband onboard if you don’t feel up to exposing yourself & baby to her ?
He may not be inclined to stand up for himself (I will try not to sound bias regarding my feelings about easygoing people too much) but if he were to, do you think he would like less time with his mother, or would he more prefer you to keep the peace ?
If it’s the first, I think you have a better chance of discussing this with him in a more frank, open manner that his mum really shouldn’t be involved in baby’s life due to her specific behaviour.
If it’s the 2nd then you will likely want to tread more carefully & not give ultimatums etc...perhaps you could reframe it as coming up with some rules for you both about safe handling of the baby when visitors are around ?
She should not be allowed to hold him or be in a room alone with him I feel. The forced opening of the eyes & throwing a blanket over him sounds particularly worrisome.
If your husband was to secretly support you but be unable to stand up to his mother, would he support you taking the lead here?
Next time she asks to hold him “I’m more comfortable if I keep holding him thank you..”
She continues to persist - keep declining
Then she will whinge & whine more to escalate her upset - at this point you can say “look MIL I was trying to not to hurt your feelings here, however we have some serious concerns regarding your abilities to care for this baby due to some concerning behaviours we’ve witnessed from you since his birth. So if you don’t mind, from now on only myself & husband will do X / X / X”
She carries on about how much she minds - “well we’re sorry you feel that way & hope you can understand that being good parents & keeping our child safe & secure is our utmost priority. While am sure we won’t get it right every time, am confident this is the right decision for us & we hope at least this way you’re able to still be involved & present in baby’s life.
If she swears at all - “MIL! Wash your mouth out with soap!”
It should be your husband who stands up to her, but that’s a side issue...it sounds like you have married him knowing this is his character type, so in this situation I have not advised him to “grow some balls” & instead given advice based on working with what you have & not trying to change people’s personalities.