Preparing them for what to expect of you and what is desired from them for the birth will mitigate 'disaster' - whilst DD is little and can't communicate with many words, she can understand a lot more than what she can articulate, so don't be afraid to get a bit 'wordy' with her about the birth. I think that even highly-strung children can adapt very well to a birth situation and realise that something momentous is happening. My DS was awake for DD's birth and lost the plot about half an hour after she was born and had to be put to bed, but that was because he had refused to go to sleep earlier in the night when labour had started He was mesmerised by what was happening to me and how his sister had come out into the world. Sure, he DID want to hop in the birth pool (and we let him), so that kept him happy and involved. He was also feeding me nuts and water while I was breathing her down. He was a bit older, at not quite 3.5yo, but I think the principle holds for younger children. Keeping them involved will work out better, in the long run, for their adjustment, than planning for them not to be there.
Sorry, I've been out of the loop here, but is there someone trusted you can call on to be your support person for the kids? We had my close GF come to film, take photos, support DS and maybe us (if we needed, but we had two midwives, so wasn't really an issue). That worked out so well on so many fronts, and I still can't believe I had that many people there - more than I thought I'd be comfy with, but as it was just how many we needed it seemed to be right.
DS was also at the appointments and heard heartbeats and the midwives involved him in the conversations. I don't think it was his age, I really think it was the preparation and final involvement that saw him transition smoothly to the new dynamic. He knows exactly where she came from and feels part of her existence, and that makes it easy for all of us
Sorry to be annoying, I can't help but feel that MORE involvement is your ticket with DS and DD