The law does not require the team to accept the findings or implement recommendations from a specialist in the private sector.
The law does require the school to respond to your concerns about your child's educational program.
The law also requires the IEP team to consider the results of any evaluation you obtain.
What does "consider" mean?
The dictionary defines "consider" as "to think about carefully in order to arrive at a judgment or decision, especially with regard to taking some action."
The federal special education regulations impose an "affirmative obligation" on the school to consider the results of the evaluation.
In one case, a federal court ruled that the school's refusal to consider private evaluations was a serious violation of the law and denied a child FAPE.
If you get an evaluation from a specialist in the private sector, ask her to attend the meeting to discuss her findings. If the evaluator is available to describe the child's needs, program, and what will happen if the recommendations are not accepted, it is more likely that the IEP team will accept and use the results.