Your situation reminds me a lot of the one my long-suffering grandmother found herself in. Like you, she had an overbearing mother-in-law (and sister-in-law) who lived nearby and thought nothing of stopping by unannounced. This went on for so long — until they both died! — that it was still happening by the time I was a child and my great-grandmother and great-aunt dropped by unannounced to visit me when I was in town. If my grandmother were answering your letter right now, she would warn you not to let this go on for two generations, and to set clear boundaries now.
Obviously, you’ve tried setting boundaries by politely asking your MIL to pre-schedule visits with you, but she has ignored that wish, so you have to be more assertive, no matter how much you fear creating tension. Trust me, there will be much, much more tension between you if you allow this behavior to continue indefinitely. For the sake of your sanity, and your relationship with both your MIL and your husband, you have to put your foot down. Explain again that you appreciate how active your MIL wants to be in her grandchild’s life, but you simply cannot have her stopping by unannounced anymore — that your schedule doesn’t have room for unplanned visitors. And then, the next time she ignores your wishes and comes a’knockin’, don’t answer the door. Let her ring and knock and call your cell phones, but don’t let her in. Later, tell her that you were taking a family nap and didn’t hear her. Another option is to open the door and say, “Oh, I really wished you would have called first! We would have saved you a trip over since we’re actually on our way out.” And then — and this is crucial — get your coats on, grab your diaper bag and leave your house. Get in your car and drive away. If your MIL asks where you’re going, make something up — you’ve got a pediatrician appointment or a play date or tickets to the freakin’ opera. It’s not enough for you to tell her that you’re too busy for unannounced guests — you have to show her.
Employ these tactics every single time your MIL comes by unannounced until she gets the message. If she expresses resentment that you’re never available when she comes by, remind her that by simply giving you a head’s up, you’ll make sure you’re available so she can have plenty of time with her grandbaby. Maybe you’d even like to set up a regularly-scheduled time she can stop by — say, every other Friday night so that you and your husband can get out and have a date while she babysits. You say you moved to your in-law’s area so you’d have help and you’re still waiting for that help to materialize. Maybe, if you’re a little more explicit about what your needs are, you’ll have better luck getting the help you crave. It’s obvious that your MIL wants to spend time with your baby, so use that to your advantage. Give her some times that work for you where she can see her grandchild and you can have a date with your husband, get some errands run or do things around the house. Win-win for everyone, no?