I struggle with these posts because whilst I can sort of understand the point of 'dont have kids with someone who already has them if you want to spend lots of time on your own', I also hate the way such emotive language is used to manipulate the discussion into something so much more unreasonable sounding than it actually is. 'Sent away', 'shipped off' and so on...
It's not being 'sent away' to simply stay at your mother's house, your home, for a little while. You're not being shipped off to stay with a stranger or a relative you barely know, sleeping on a pull out bed whilst Dad and SM spend a week on their own. You're in your home. You aren't being sent away anywhere. People say it that way because it makes it sound worse than it is.
In reality, we've had lots of instances through the years where DSC have stayed at one house or another longer than they usually would due to various things. Family emergencies, illness, miscarriages (both me and their mum), births and so on... It really doesn't need to be some huge dramatic thing of 'shipping off the children', it's just life.
I agree that siblings will want to meet fairly soon and so I would hope that they'd be able to visit fairly soon, even if not staying over, but I don't think a few days to allow a woman to recover, especially from a traumatic birth, is unreasonable at all. There really are some occasions where an adults needs should be paramount.
You can talk about what happens in nuclear families all you like but in reality, blended families aren't that. The children have two homes, two parents and the availability to give a little flexibility when needed due to this. And it's also not true that this never happens in nuclear families. I went to my grans for a few days when my mum had a very traumatic birth. I wasn't shipped off, I'm not emotionally scarred or anything. My mum, an actual human woman with needs and feelings, needed some time to recover and to be looked after herself for once. It's hardly the end of the world.
I would always expect us to give flexibility like this to my DSCs Mum (and we have in the past) and I know she'd do exactly the same for us (as she has in the past). In fact she's doing so right now, I am in early labor right now, I was sent home in the night to progress here. We were supposed to be having the DSC and she has said absolutely she will keep them until baby comes so we don't risk having to rush them back to her in the middle of the night and so on. No drama, no anger, just grown ups working together and giving each other some flexibility and understanding. And because their mum is so understanding about this stuff and because they know their Dad and I love them too, they don't feel shipped off anywhere or sent away, they just know that right now something is happening at Daddies which means they need to stay with Mummy instead, no one bad mouths anyone and explains it to them properly and they are fine. We have done similar as I say the other way round in the past.
I really think the way people react to this stuff affects how the children then react themselves personally.