R.
In my experience of teaching in Private schools is that they tend not to have the expertise, specialist teachers, experience or funds (and in many cases, the inclination) to help kids like your daughter. That is why I moved to public funded schools. I know other private school teachers who insist that children with learning difficulties have better opportunities for help in the public school system - they have reading specialists and are more able to aply for and receive extra help. Kids in private schools usually have to pay for speech therapy etc (unless it is stipulated in an IEP) but those in public schools may have it paid for by the school district.
Also, bear in mind that teachers in private schools do not have to be licensed. Many are, but it is worth asking about teacher qualifications, experience and training if you are looking at private education.
Good Luck
R.