Like your daughter, I am autistic myself. In addition, a section deep in my brain, at the front of the front of the corpus callosum, has been scarred, further inhibiting my ability to experience and interpret emotion. This puts me in a somewhat unique position to respond to this question.
Unfortunately, like autism, ADHD simply means "there's something going on in that brain and we don't really understand what". It's a symptom, not a cause. With functional brain scans, we can see that there are at least six very different unusual patterns of brain metabolism that express as "autism", but we don't have the foggiest idea what they mean.
Sadly, ADHD has become a catch all for everything from "the kid's bored and the teacher doesn't know how to deal with boys" to "there's something seriously wrong here". Dr. Daniel Amen often talks about his nephew who, as a young boy, started expressing unreasonable anger and violence. The "something" in that case turned out to be a large cyst.
Assuming this boy truly has ADHD, then it is not purely a matter of discipline. There is something either mechanical or metabolic (or both) going on in the boy's brain that he cannot control and the doctors do not fully understand. Like autism, ADHD may or may not respond to medications. Kids may or may not outgrow it. Parents are often blamed for something that is outside of their control.
One of my young associates has ADHD. Normally, he is one of the gentlest, politest, and kindest people I know. However, from time to time under certain types of stress the "switch flips", and it is not always obvious to those around him why. Even though he weighs about 80 pounds soaking wet in winter clothes, he scares adults around him when that happens.
Fortunately (or not), I am one of the few people that "get" him. I can actually point at an anatomical chart and say "this part of my brain is damaged, and the result of this damage is these symptoms", which largely mirror his own.
The result of my own brain damage is reduced verbal capacity, and inability to recognize normal social cues, prioritize, or maintain focus. With next to no ability to experience emotion, to all appearances I jump from incredibly patient to all out rage with no warning. Does this sound a lot like ADHD?
As a parent, your first responsibility is to look after your own children.
As a parent of a child with autism, you can probably empathize with your single mother friend better than anyone else. However, you might want to arrange to meet without the kids, with separate babysitters.
