Both parties in the wrong here.
The parents chose to have their child wait over an hour for food, of course she would get "fussy".
The owner should not have screamed at a child, and sounds very irritable.
I have been in cafes where kids run around screaming for 30+ minutes, and staff talk to the parents a few times and then ask them to leave. Or they talk to the parents once, and shake their heads when it continues. Some parents don't care.
I have also been in cafes where a kid is having a bad day/moment, and the parent is trying to placate/help them, and staff approach and ask if they can help, or if the parents would mind moving to a corner table, or leave (depends on the age of the child I guess).
i have never witnessed anyone working at a cafe or restaurant, etc, yell at parents or children... oh wait once when a kid was running around and ran straight at a waiter and tipped their bowl over- it was clearly something hot as the waiter yelled- it wasn't actually at the kid though.