Hi, I think (as a mother of 4 kids, eldest son is 8) you can try to talk to May when she is in a good mood and relaxed. You can sit with her and ask her to help you with this situation. This makes her feel important and probably, she would act like adult. You should look deeply into her eyes, then describe how upset and devastated you feel when she has her tantrums. Ask her what you, as her nanny, should do to minimise such situations. Then let her talk. Most girls are very emotional, let her lead the conversation. In her speech you may hear some clue, which will be an answer for you.
You already know it, but I write it however
- you should show her understanding, love and grown-up behaviour. When she acts bad, look at her as you would look at the sick kid.
Every misunderstanding should be talked about when the dust settled. After every
tantrum, may be after hour or two, you should talk to her (do not be afraid, it should be done) and show her your point, she should see the situation with your eyes and you should try to do the same. You should talk from heart, describe your feelings about sweaty legs without socks, about extra sugar before dinner and so on.
About her envy for friend's new things: let it for month or two. Do the talking thing.
Later, after she becomes sane again, cuddle her and compassionately ask "I see, it was hard for you, my darling? When I was at your age, I was upset too when somebody have cool things, I want them so much!" Then let her talk, just listen. She may say bad things, you should not argue with her. This bad feelings should be set free. After she's done, look at her with love (remember! sick, ill kid!
and say, I love you, you are great kid, all will be fine. It would puzzle her.
Now about her pressing requests: if she do so, try to humour her: imitate her whining, smile, then cuddle and tickle her - it may switch her attention. Then put your idea about the next activity - do something together: read her favourite book, listen to music, may be she can help you with some routine.