When my DC were small, DS had a very good appetite (always and still has!). However, the little girl next door would eat nothing - apparently. If she didn't eat her breakfast then her mum would give her a bag of crisps at 10.30 because she worried she had had nothing. Then, of course, she wouldn't eat her lunch and so on.
She asked if the little girl could come in and have lunch with my DS and, if she saw him eating, she might eat too. I did say, don't give her anything in between meals except fruit and a drink. I don't think she ever ate much, but grew up fine (she is a headmistress now).
It sounds as if your DGD knows full well how to 'press everyone's buttons', however, I don't think she should go to bed without anything, even a bowl of her favourite cereal and milk, or bread and butter and a drink of milk.
I would feed her her favourite (healthy) meal every day for the time being (does she like spaghetti bolognaise?) until she got sick of it and wanted something different.
If she screamed for an hour that's probably why she ended up coughing. Ignore tantrums, just keep an eye on her to make sure she is safe! The twos and threes can be a trying time, but it's no good punishing them for having a tantrum, they are just expressing their frustration and can't articulate how they are feeling.