ETA - It's totally normal for a contact lens to rotate around while on the eye. It's just what they do as one is wearing it. An astigmatism means that the curvature of the eye is irregular, so light hits the eye at different angles. The doctor takes measurements on the curvature and applies them to the contact lens. The lens is shaped specifically for that eye and has weights inside it to make sure it stays in place. So my contacts are heavier on one side, and that's the side that stays down so that the lens sits in the correct position for my curvature. If I lie down on the couch to watch tv, the lenses will rotate and I won't be able to see as well (so if I really want to do that, I have to put on my glasses).
It's possible her astigmatism is very strong and difficult to fit a lens, but if her lens is rotating, it means that the weights are wrong.
Original Answer - I have astigmatisms in both eyes. My doctor was well aware of this before I asked about contact lenses. I could be wrong, but my initial thought is, no this should not be difficult at all!!!
The doctor should have made notes and taken measurements on her eyes and done his/her "best guess" as to exactly how to shape the lens for each eye. A "trial" pair of contacts is then ordered for her to wear for a few days followed by an appointment just to check and make sure the fit is right. If not, adjustments can be made and the correct fit ordered.
I have been to 5 different eye doctors (because I've moved around), and they have all followed relatively the same pattern. Honestly, if they've been practicing for a few years, they usually always get the fit right on the first try.
I'm really having trouble with the fact that your doctor seems to have just now realized that your daughter had an astigmatism. How was this not discovered at the first exam?