I'm fortunate in that both my in-laws and my parents just aren't that bothered. They'll come when we invite them and not want to stay very long. My parents live 20 miles away and my in-laws are in the same town, so it's just a short trip for all involved.
To give an outside perspective, here are my thoughts: their babies are having babies and if you think it's been enough to blow your mind, think about how it's frazzling theirs. Think about how it will feel when, in the blink of an eye, the baby that's curled up in your tummy right now... has a baby. 🤯
It doesn't mean that MIL is behaving fairly or correctly, but having the empathy to understand why someone else is going off their rocker can help you to feel calmer about it.
With that in mind, consider offering a compromise of 4-5 days. You and DH can deal with her together. It's his mother but it's your choice and you're family, bound now by more than just marriage but also by a blood tie.
I promise that when baby appears, minutes, hours, days, weeks and months will blur and become almost indistinguishable. You won't look back in 16 years and think "I wish I'd held the MIL off for 48 more hours". So just let the old bat come and visit. You're holding onto this fiercely now, out of principal.
I can tell you categorically that it doesn't matter anywhere near as much as you think it does. Don't waste anymore energy getting upset about it. Have a snack. Watch some Netflix. Relax. Offer her a compromise.
If all else fails, and she isn't open to peace talks, you'll have to keep the birth a secret from her for a few days. But this is a nuclear option that may explode into a row, while you're trying to master new motherhood. Infinitely more stressful in the long run.