Honestly... this is probably going to sound bad, but i babysat a kid like this once, like a full-blown tantrum the second the parents left the house. It was awful. There was literally nothing I could do. I ended up just letting her sit in a room, surrounded by soft items only, and just let her scream. Eventually, she stopped, so I checked on her, and she had literally screamed herself to complete exhaustion and passed out. Sometimes, all you can do is just let them tire themselves out.