Poor girl!
Yes, it has just about all been said by the very wise contributors on this site but I wondered about a few further points:
it is your husband, home and baby (perhaps not in that order!); your MIL is probably jealous/lonely/feeling marginalised (probably enhanced by suspecting your own mother is with the baby all the time. Your MIL's physical distance may be distorting facts) however she is also devoid of love and empathy for her family to put you in this situation.
Enlisting fire-proof support from your husband, ensuring he won't crumble under pressure from his mother, is the first thing to do.
If that is in place, could you suggest that he sends these comments on to his mother? Or perhaps leave them laying around on this open page during a visit (which, incidentally is twice as long as should be, for both parties... as has been written, people are like fish!). When your MIL is in your home she is welcome to do tasks as requested by you. Otherwise she is a guest and should relax as such.
Whatever you both decide to do, it is your MIL (unless there are facts we are not aware of) that needs to make major changes if she wants to keep a relationship with your growing family.
What is your FIL's role here? Does he acquiesce to his wife's every whim? If so, your MIL is just a control freak and it wouldn't matter whose home she was in - she would be the same character, so don't take it too much to heart. Perhaps enlisting his support, by having him take your MIL out for a few hours a day during a visit could help a little?
Stand firm (oh dear! Our Skype has broken.....we'll have it fixed 'soon'........) and tell your MIL that although you do love and care about her, she is risking a fractured relationship with part of her family. She may hope that your son will 'take her side' if push came to shove in an argument, hence your talking the whole situation through with your husband, making him understand quite how sad (and cross!) you feel.
Re painting metal bistro garden set
Army horses loose on London streets