I have no personal experience with this, but this article seems to have a lot of great information: http://www.aafp.org/afp/2006/0201/p469.html
A few things I noticed: the article recommends changing diet to include little or no dairy (specifically from cow's milk), and to include lots of high-fiber foods - not fiber supplements. Which isn't to say supplements would be ineffective, it just sounds like it's better to change the actual foods to include a lot of veggies and not a lot of dairy (and possibly reduce gluten).
Second thing I noticed: at the end, the article says that if functional constipation lasts longer than 6 months, the child should be referred to a pediatric gastroenterologist. I'm sure that you guys have been working with doctors, but have you seen a specialist of this type?
Third thing: does your daughter really understand what is happening and why? The article suggests explaining to children who are old enough to understand, and it suggests that some behavioral therapy accompany any medical treatments. Have you tried these things? It seems the fear of painful bowel movements is key here, and if she can understand that the pain is caused by refusing to poop, she may be more willing. The article specifically says that after a disimpaction the goal is to have 2 soft stools per day (with the help of oral aids) for six months (which may require staying home at first for comfort purposes).
Fourth: the article lists other ways than enemas of disimpacting that are non-invasive, they're just slower. If your daughter needs disimpaction again, maybe explore one of these options so it's less traumatic for her.
Finally, this seems not to be a "solved" problem, medically speaking, as the article indicates that about half of children with this problem don't improve even after 5 years of treatment, and a third don't improve after 7 years of treatment. This observation is not meant to be discouraging, but rather to suggest that if you find a doctor with innovative solutions to try, you might want to.