I cant help but chuckle. Since your DD has not started private school, I doubt there is a court in the land that would say she has to go to private school.
I'm not sure how it works with public schools where you are, but most public schools are not pick and choose. You go to the school that your residence belongs to.
Have you considered looking into a charter school? My kids go to a charter school and many of their classmates come from out of district. There is not much difference in our charter school from a public school except that the staff is non-union and operates on a reduced budget.