There was a couple of children in my family who acted exactly like this, no therapy was taken as it wasn't really done in those days.
Both women are now categorised as a sociopath.
Her behaviour, the hurting her brother, both when he was in a crib and pushing him over is worrying, I can't believe neither her mother or father are doing anything at all to change her behaviour.
She needs to be in some form of therapy and have someone listen to what's really going on with her. For her to be having certain thoughts about peoples looks and weight and the houses they live in, this is a lot for someone her age.
As her step mother who has actually looked after her as a young child, you are not silent in this, you can speak to her teachers. Perhaps this behaviour is happening at school? Something needs to change.
And I agree with others, if you leave her out of the holiday, the jealousy that she's already voiced and expressed, will only grow. It's not the ideal situation to have her behaving like that, but she's one of your husbands children too, and you wouldn't leave your own behind.