There are three things wrong with this:
First, let us take her premise that God inflicted autism to punish her; that God punishes an innocent child for something the child did not do. That kind of contempt for what is fair disproves that such an unjust God would keep His promises to give us paradise after death and it make it futile to pray to or try to get along with Him. It is almost akin to God punishing someone in the antebellum South by causing offending parents' baby to be born with a wrong color of skin, a color that society arbitrarily ascribes, in its junk science, to inferior genes.
Second, it demonstrates a form of racism against autistic people who suffer no comorbidities, autistic people are presumed an inferior form of human, a defective untermenschen race, in some cases, life unworthy of life as we have seen in how parents who kill their autistic children are treated more leniently than most other killers.
Third, if she wants to speak with authority on autism, and claim there is such a thing as a cure, she must earn that authority by doing the years in graduate school and possibly medical school learning the science and what it can and cannot know. She is not trained to diagnose that her son is cured.