Let's get this straight.

Autism is a condition no one can have control over. It is something no self-respecting parent would their child to have, nor get rid of. The stress levels they get with a child of such condition are way off the roof.
I highly insist you read up more on Autism and how parents have to try to cope with them.

You speak of being unfair you have to deal with neighbours like these, what makes you think it's "fair" for them to have such a child? Or to deal with them on daily basis, for the rest of the child's life?
They already have a shitload of stress to deal, and now with you "telling them make/let the kid play something else" and as if you know more than they do on how to handle kids with autism when you're yet to be a parent yourself? How can the mother not be defensive when having to face with people like this?

There's nothing fair about the situation. You did not chose to have such neighbours, nor did they chose to have a child with such condition. Don't label them as bad neighbours.

Some already said, either you deal with it, or you move out. Or if you want to be a--holes, get your neighbours to move out.

You mentioned you've already spent a lot with renovation. You can either spend more into looking at ways to further sound-proof your unit (if possible, i.e. thicker windows, door seals, etc.), or weigh which is more important = your mental health (as you've mentioned) or the money you had spent on your renovation.

Either or, there is no easy way of dealing with the situation you are facing.

Sorry, the more I read your post, the more upset I became, as if you are blaming the problem on your neighbours. But understand this, it's not the neighbours who are intentionally putting you through this, and that also they are dealing with the same thing you are. Also note this is something you can escape from, but not themselves.