Help, I have a 10 year old boy who is highly intellegent and very well behaved and an 8 year old girl who finds school a struggle and has a split personality. She can be so lovely and people think she is a little angel. Then if something isn't going her way or she you ask her to do something she doesn't want ,she changes. It has got to the point where she doesn't like having a bath if it means a hair wash. She refuses to eat her dinner if she doesn't like the look of it. She can play really nicely with other kids and her brother but if she doesn't like the rules she explodes. We have door slamming, shouting at the top of her voice as if we are all deaf and saying she will leave home.I try to give her attention and try to disaplin but she is just not bothered by anything. We live abroad so she speaks 2 languages and enjoys animals and dance. The school have said she seems good there but sometimes a little lazy.she always tells me that she has very few friends and nobody likes her. I am aware that she has a lot to live up to in the school playground along side her brother as he is popular with all he meets. Is this just a stage of 8yr old girls or am I going wrong somewhere?

I wouldn't trust it to a stage because if left as is it could only get worse.
When she complains that she doesn't have many friends point out to her that people do not like being around people that can get so upset so easily. I am not sure what you can do to get her to change but you can not give in to her. She needs to learn there are consequences whether it is go to bed hungry or kids making fun of her because she didn't wash her hair.
Hopefully she will realize soon that her behavior is only working against her.

She may need special mom/dad time, away from her brother. At this point, he has support and approval from his friends, teachers and parents. She appears to be acting out for attention. I realize that you would like two easy children. What you have is a bright boy and a bright girl. The boy is approved of, the girl feels left out/not approved of. She will never be like him. She will never have two years practice on life ahead of him, never be male, never be the first child/star of the family.

She needs you now, before she finds approval from those who will give it to her from "the outside." I was the youngest, behaved much like your daughter and hooked up with very bad people. Children seek acceptance, regardless of their gifts. They will act out and align themselves with whoever shows "love" to them, as they are.

Have you looked into personality type testing? It's possible that your daughter has one of the rarer personality types, which can make her feel isolated. She may also have difficulty reading social cues, which is a skill that she can learn, even if it never comes naturally.