I don't have a daughter that age yet, but my younger sister used to do this to mum. Mum used to just tell her that she must eat something and would give her a sandwich for dinner. She then had the option of what we were eating or the sandwich. Obviously it isn't ideal long term but at least she would be eating something in the meantime. Would she take childrens multivitamins?

Sorry, not a foolproof answer but at least an idea!