Talking and having a healthy discussion would help immensely. Coming to a consensus that each one will talk their views and ideas rather than have an anger outburst will help.
1. Firstly try talking to the child. Find the cause for this reactive behaviour. Sort out issues, if it is related to her peers, friends, school or school work.
2. Talk kindly to her, about the rights and wrongs rather than passing comment and judgments. Children become more defiant and sensitive when commented upon.
3. Then, about her response to a task, charting out a plan of action and plan a daily schedule would help immensely. Brief her about the importance of a daily schedule rather than advise and suggest things to do.
4. The child now being 12 years is undergoing a few hormonal changes and this could be one of the reasons. At this phase, children are undergoing a lot of physical changes and they find it a complicated to adjust to this new change. At this age they need all the support and assurance that things are fine.
5. Then coming to the part where she is taking out the anger on her younger siblings, she once identified herself with them as a child, the changes in her could be making her feel a little different.
6. Staying calm, talking to her, explaining and making her feel that she is being understood would reduce the behavior and then gradually this will fade out.