I'm a bit mixed on the situation.
I have a teenage sister on the autism spectrum, and I completely emphasize with the family. Anything can set off my sister, and it is difficult trying to prepare for every possible issue that might arise. If we are eating at a restaurant, she can become overstimulated and might need to leave even before food is brought out so that the entire restaurant doesn't have to listen to her melt down (these situations have been "interesting" the past few years because of my diabetes. I take insulin for my food, she decides that she's had enough, and I now need to decide whether to get my food but have her melt down in the process or leave and risk going into severe hypoglycemia before I have a chance to get home and eat something). Even when we drove down to Disney, we ended up getting a flat tire on the way, and she almost had a melt down during that time because of factors we could not control (a hygiene product was irritating her and she wanted it changed IMMEDIATELY). We try to prepare for issues that might happen, but we never know what might set her off. Something as simple as the tag of her shirt irritating her could transform her from her jubilant self into Godzilla.
On the other hand, I feel like the mother could have discussed her child's needs more appropriately without making it seem threatening. Saying something along the lines of "My daughter is on the autism spectrum, she's starting to act up, and I'm concerned that she might become disruptive to the other passengers if she doesn't have anything to eat; due to her sensory issues, she will only eat foods hot. I understand you might not have any hot foods available, but it would be appreciated if you could help us in any way. I'm willing to pay for a first class meal if possible" is more appropriate than saying "How about we wait for her to have a meltdown and then she is crying and tries to scratch -- and then you'll want to help her". I completely understand that she was most likely stressed out about what was happening and might not have been able to appropriately express her concerns, but the way she said what she said almost sounded threatening.
I'm trying to think of what could have been done to prevent this situation, and it's been difficult. There have been times where my sister also would not want to eat at a time that we're eating. It might have been possible for them to take a to-go box of the food and ask if they could heat it up on the plane, but I'm not 100% certain that would be possible on most planes. I don't know why they decided to continue to make the emergency landing once she was calmed down. It doesn't seem like she was continuing to be a threat to the safety of the rest of the passengers and crew.