Kid sounds really, really autistic to me. There are kids who match this exact description at our elementary school. If only her kids were older, she would have so many more resources at her disposal. These kids have their own special ed teacher to hang out with them and give them undivided attention, there's an entire department they go to for calm down exercises, they get constant notes and updates and analyses to optimize the strategy at play, it's amazing what public schools can do for families who struggle like this.