The owner of the diner should have spoken to the parents politely about their child's crying before escalating the situation (which maybe she did, we weren't there so we don't know). It's not okay to just start shouting at a toddler.
That being said, the situation was the parents' fault in the first place. If you cannot quiet your child in a reasonable amount of time, leave the public eating place where you are disrupting everyone else's meal. Sticking around while your child screams for an hour straight is unacceptably rude, inconsiderate, and just fucking obnoxious.
By the way, I do not think it is wrong to politely admonish a stranger's child when they misbehave in an establishment you own. It's not okay to do so in a threatening or frightening manner, but if parents refuse to do their job others should not have to suffer in silence.