And what about when the time comes, when you NEED her to be able to babysit, because believe you, me, whether you like it or not, and whether you think you've got all bases, and scenarios covered, that time will come.
I totally get the respecting boundaries thing, and also the childcare aspect, however - in order for her to respect boundaries, you need to set them, and you haven't done this, you have just slammed the door in her face - you're sat there all frustrated and annoyed and, almost, resentful - I daresay, she is sat feeling the exact same and, whilst all his is going on, your child is missing out on a valuable relationship. So whilst you think this is a 'win, lose' situation, in your favour, it's actually a really sad situation to be in.
How does your DH feel about this? (And remember, without your MIL, he wouldn't be here, and neither would your child)
Your child is lucky to have grandparents, and ones who are so willing to be involved, even if a little bit overbearing.
I don't have the most amazing relationship with my MIL, we are extremely different people, have different approaches to parenting, I've been undermined at times, she's upset me at times, and I've bit my tongue, but I just suck it up, because she loves my kids, and they love her, and I'm lucky, and they're lucky to have that relationship - who am I to stand in the way of that?