I was told something as a child - there's one persons side, another persons side and then the truth somewhere in the middle.
We all see things differently and OP will see it differently to her MIL. That happens but surely there is a way past it.
OP I was with you all the way until some of your later posts and you do sound really controlling. It is also upto your partner what he wants to do with your child and he is allowed to take his baby to see his Mum without you.
It is coming across that it's all about what you want and not your partner too whether you mean to or not. I know you've said he agrees with you but that doesn't mean that he doesn't want to go and see his Mum with his baby alone.
I understand that this has probably built up over a while and yes she's said things that she shouldn't have and she should have not said that and apologised.
I really think that it would do the pair of you some good to sit down and talk it through. I know that you say she'd start crying but I honestly believe it needs to be said and at least then you could say that you've tried. If she does cry, stop, and then talk to her when she's stopped and repeat if needed. She may be upset but if it is controlling like you said then make sure you say it all and that way she hasn't controlled you.
If you sat down with her, told her exactly how you feel, how you felt when she mooed at you and if she still doesn't listen then I think you have every right to do what you're doing but I do believe that she does need to be told.
Nothing has been said about your FIL(sorry if I have missed anything) - is he just as bad? do you know what he thinks about this?