I agree with jdm it sounds like a child /parent interaction problem , also the oldest child may be jealous of the younger one who perhaps doesnt get into hot water as much as she does.Mornings are always a problem my suggestion is you wake them up earlier instead of rushing them around let them be less hurried when they are still sleepy, this is very common in a lot of households. Instead of 'telling her to do something give her a choice, instead of demanding she cleans her teeth or brushes her hair which inevitably gets a No response, say would you like to do it now or after breakfast ,accomodate her if you can, dont feed into a tantrum and get into a power struggle, if she yells let her walk away.Focus on her positive side and praise her when you see her doing something right. Do things with her ,some cooking some shopping one to one things. ask Dad to help with outside games and activities.board games are fun.
So from reading some posts here it must be the Parent/Child dynamics going on here.
Maybe, maybe not. Another option is anxiety - your daughter might suffer from anxiety but feel comfortable enough in your home to act/react to her frustrations and/or fears; whereas at school, the environment might be so scary that she "appears perfect". I might suggest you goggle the phrase "children and anxiety" or "anxiety disorders in children" or similar words/phrases to see if this issue might be a possibility. If you feel that anxiety might be the issue, please let us know as anxiety is very common in children and highly treatable. Just another suggestion ....