This is bigger than the birth! OP, you have to find alternative childcare because if she knows you are in labour she will harrass you.
Sort it now - how far are your inlaws? Could they take 1-2 of the children and one go with someone else, a school friend? Most people are very willing to help in this kind of situation. Worst case scenario - you go into labour in the middle of the night and DH isn't there. Plan for that. Is there really not a friend who can help along with PIL? If really not, a local childminder - massive fees, but you could have an agreement that you can drop them off? Do you have quick births - the likelihood is that in real time, you'll have time to sort this out without a complete panic.
But in answer to this:
You are people pleasing and teaching your children to do the same. It’s not good.
What’s the alternative? - The alternative is to do exactly what you dismiss out of hand above, but is obvious to anyone else on this thread. You say you're able to stick up for yourself but you don't want to do it, as your relationship is 'fairly volatile' - so, code for she screams and gets her own way because you feel that's easier. Is it? You said her ignoring DD for the first 18 months was great. So what's the problem? Fuck her off. SHOW your kids that people who threaten, scream and bully don't get listened to. Tell her you absolutely won't have her there because last time, she made it really stressful and you hated it. If she wants to refuse to look after the kids, fine, you won't be seeing the new baby then.
A word of warning, people like this have an absolutely negative effect on the children around them. You think your kids have great relationship with her. They don't - thry watch her bullying and dismissing you and they're learning that you're smaller and weaker than the big powerful granny. It's very dangerous to let someone like this be close to your kids and have their ear, and their trust. You just wait until they're bigger and she can use them to needle you - 'Oh no you don't have to listen to stupid Mummy. Go out with your friends all night if you want to - I'll give you a key to our house and you can come to granny whenever you want.'