I woke up during my appendectomy. I remember it very vaguely, and I'm only sure it wasn't a dream because I woke up in the recovery room with restraints on because I had tried to sit up during the surgery. I did not have anything like the experience of the little girl in the story, but I was twelve, not four, and was having laparoscopic surgery, not filet-you-like-a-fish surgery. I also think the surgery was complete when I woke up and they were just putting in the couple of dissolving stitches and sticking on bandages.
Overall, I'm skeptical of "memory recovery" during hypnosis. Although it is clear that peer-reviewed trials support the utility of hypnosis in many applications, including even anesthesia for mild procedures, it is also the case that hypnosis could make a person susceptible to false memory syndrome. The anecdote which opens this article is moving, but I'm a little suspicious of how perfectly the explanation fits her symptoms -- many people with life-altering mental illness seek the "silver bullet" explanation of WHY there is something different about them, and are exceptionally ready to create false memories that would make all the pieces fit.
That said, it's certainly not impossible that a young child could suffer lifelong trauma from waking during surgery. However, I remembered the waking up immediately after the surgery, not years later, and I doubt that even at four such a powerful experience would leave no conscious memory, but leave a "repressed" memory. One would think that the child would have at least explained it to her mother at the time, even if she later forgot the acute, conscious memory as she grew up.