I'm planning a birth centre birth, and leaning towards having DD present. She'll be three and three months when the baby's born. I figure we can start her off with us - DH can bring his laptop with headphones, in case she gets bored, and we can have snacks and so on. I'm doing Hypnobabies, so hopefully I'll be calm - I was fairly restrained last time, even though I didn't feel calm! So I'm not too worried about screaming or anything.
Anyway, ideally she could chill out in the birthing room, go to sleep in a corner somewhere if she needed to, and wake up/participate in the actual birth part. She's seen plenty of birth videos on YouTube, and is pretty cool with it.
On the other hand, I'm prepared for the possibility she might either get really bored and start causing a fuss, get upset if she sees me in pain, and/or just disturb my hypnosis and get in the way. In which case, we'd go to Plan B - get my mother to pick her up. It's no more trouble for Mum to come to the birth centre than to our house, so why not? So I don't want to be dogmatic about it either way - we'll just play it by ear and see how she goes in terms of tiredness, boredness, behavior etc.
I do know of a few families in which the older kids are always present at the birth of the new baby; and they don't seem traumatised at all! I assume they prepared the kids for it pretty well beforehand, though; and these are families that are pretty low-key about life in general, so maybe that's why the kids just took it in stride? I was present at my little sister's birth and it was a great experience, but then, I was much older - 12 - so I guess that doesn't count for your purposes.