I have a 10-year-old daughter with Down syndrome. She has some similar issues as someone with autism, especially on a bike.
She was afraid of the Adams trail-a-bike - until I finally got her on it. She loved it instantly.
So that she's stable, and also just in case she decides to just get off of it mid-ride (something I can really see a kid with autism doing) I put this seat-rest with a strap on the trailer:
http://www.amazon.com/Trail-A-Bike-1.../dp/B000SMS7IC
She isn't into pedaling her own bike much, but she loves to make me do all the work.