Hey Karen:
I actually was always told that if you have a milk intolerance/allergy (which constipation can be the only symptom), that so many can handle 1% or 2% milk because of less of the fat.
It doesn't make sense she would be more constipated on it, unless it is like anything else, your body has to get used to the change (just like a formula change).
Did the constipation start with potty training by chance? Oh wait, you said she has always been constipated.
Maybe the allergy test will give you some answers, but she could still have an intolerance to it.
BTW: I used to give Zach PlumSmart juice everyday. It helped him a lot and tasted a lot better than prune juice.