I don't have experience with putting one of my children on the SCD (I myself am on it), but I do have experience with putting one of my children (at age 8) on a modified diet due to food intolerances. I needed him to stick to it, even at school and out of my sight. I offered him a motivation-- what worked for him was that I told him it would give him a quarter a day for each day he would stick to it, and that it adds up over time (it really does, but it was worth it for me!). I would pay him at the end of the week for the first few months, then by now it's become more a way of life, and I just give him special things every now and then.
It sounds like you have experience with food intolerances, too. What worked for you when removing those foods from your daughter's diet? It may help now, too.