Do you have insurance? I imagine that if you can find a therapist who is in-network, and not affiliated with the school, the copay would be much cheaper than $50. But maybe that's just my insurance.

Also, it's been my experience that the public school district is often not the most generous. They are often facing budget restrictions. If they deem that you don't require the services of a psychologist, then I don't know how great your odds are of getting them to change their mind.