Anonymous wrote:"Sounds good, let me know what time"
You actually wrote that, OP. Your MIL is understandably annoyed that you would go back on what you said. When people say the above, it means people call you as they go out the door, and in her case, since she lives close by, it implies you only get a few minutes' warning before they arrive.
You should have said: "Tell me a day ahead or the morning of."
I can't tell whether your MIL overreacted this one time or whether you're always a little bit off in your communication and it's getting to her.
But you know what? Be specific. Don't expect people to guess what you mean.
What? If I ask you to let me know what time you are coming over, that means you say 2pm or 3pm or whatever. Not that you can text me/call me when you are on your way.
OP - I am on your side, but I think you need to do some damage control here. Invite your MIL out to lunch, or to an activity (or three) with your LO. There are advantages to having family nearby, and there are clearly some disadvantages. If you don't want her dropping by, you need to be proactive. Set up a weekly picnic or something.