What happened during my emergency OHS was that Laura first contacted a family friend Audrey, and called up my mother in California. My mother flew up from there and Audrey picked up Jane (then 4 years old) and then my mother from the airport. KC my son was dropped off by the school bus and my mother was there to take care of both kids while I was gone. Some family friends came by to help with the animals. My father, only two months after his own emergency life-flight from a burst aneurism in his right leg, came out and helped my mother with the snow and ice.
Meanwhile, Laura stayed in the hospital with me, and occasionally called home with updates on my ever increasingly positive progress. Not having the kids there made it so Laura could concentrate on being there for me. Funny thing is that the only other time she and I got to spend uninterrupted time together was when she went to Salt Lake city for some stomach surgery, and I went with her, while my mother took care of Jane and KC. It seems that the only way we've had a chance to get to be alone together is when one of us has some serious hospitalization-level medical needs.
Kids would likely just get either bored (if they don't understand the situation) or terrified (if they do). In my opinion, the children should not visit Mom or Dad for at least the first week following OHS. You (the OHS patient and SO) are under a lot of stress from the recent trauma and probably can't handle any more stress. My own experience bore this out. While I missed the kids, I was also relieved at not having to deal with their intense needs and emotions while I myself was getting used to the shocking fact of my own OHS. I trusted my mother to take good care of them, and she did just fine. Despite my parents being divorced over 20 years ago, they worked together quite nicely, and even spent Christmas together at our house in an amicable way. Neither has remarried, so there weren't any step-parent difficulties to deal with.
My advice is to keep the number of people present with the OHS patient to the absolute minimum possible. A special friend, one parent, or spouse should stick around, and everybody else wait for the homecoming. Even then, keep the crowds down (unless you're a rabid extrovert and thrive in large groups) and limit visitors to one at a time outside of immediate family. You (the OHS patient especially) will know when you're ready for more. Even then, keep it limited.
One funny thing happened when I went back to one group. I am a member of the National Speleological Society (a caver group which works for cave exploration and conservation) and the local chapter, called a "grotto", held its annual Christmas party right about the day of my OHS. In January 2008, I asked Laura to take me to the meeting, and the president, a good friend who is aware of my punning and word-play, said, "Well, here it comes..."
I said, "I thought I really wanted to go to the Christmas banquet, but I guess my heart just wasn't in it."
I can still remember the groans and a few chuckles. Before the first hour of the meeting was done, I was done and asked Laura to drive me back home. It was the same with my rock and gem club, though I didn't inflict the same warped gallows humor on them. As I felt better, I was able to handle being around more and more people, so by March, I was able to handle dealing with the public with my rock and gem club's annual show.
I hope you get something useful out of this, and wish you well on your AVR surgery.
Chris