My suggestion may seem extreme, and I sincerely hope that some other member here comes along with a better one, but if you are not qualified/trained to teach autistic children, then I certainly suggest that you try to make it as clear as possible to the parents that their child has special needs and that they should find a specialized teacher – and then bow out of the position. Getting even a normal child to acquire enough English to satisfy its parents is difficult in Japan, and it seems to me that you could possibly endanger the child's overall learning process as well as inflame her parents.
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