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I could see admitting him to a hospital of there was a risk of harm or if he were hallucinating or something, but all we've got are random, nonviolent tantrums a couple of times a day.

This may not be helpful, but I just want to say that I'm fairly shocked and confused that they have suggested this for a child whose problem behaviors are those you describe. It seems really extreme. DD8 tantrums probably once or twice a week (no harm to objects, self, or others--but she screams and is hysterical) and while I am concerned and seeking a referral, I would never consider her behavior worthy of hospitalization even for a second, even if it were daily.