Parent of autistic child here:
UA was wrong to divert the flight. It was apparent that the child had calmed down, was not bothering anyone, and the crew was obviously not trained to handle someone with this kind of disability. I don't blame them personally, but more suitable training would have gone a long way.
Mom was 100% wrong to throw out the "scratching" bit. Once you cross that line, in the minds of FA, crew, etc it incorrectly gets pigeon-holed into the "this pax is a threat" mindset. It's the same reason that you never argue with a FA, TSA, etc no matter how wrong they are because you're invariably going to get the "do you want to fly today?" line. My 5 year old daughter still cannot drink well from an open cup - juice boxes are a requirement. TSA is hit and miss on getting them through security, but I always bring at least one extra for the TSA to open up and smell/examine/make me drink, etc. If I ever got a super-uptight TSA agent that simply refused them through in their entirety, it would be a problem. Thankfully, it never has. Could it? Sure. Is that reason for us to never fly? No.
I've flown with my daughter multiple times and she's never had a problem. However, despite the best planning, sometimes things happen and it's not the parents fault. I wouldn't expect anyone who doesn't parent an autistic child to understand this so I won't take personally several of the ignorant comments I've read on this thread...because I don't think it comes from a place of malice, merely ignorance.