S.T.
I do have to agree with the people who said to be stronger with the discipline... Taking things away seems to work for my 10 year old. In addition to that, it sounds like she may need some private time with you. She is at a stage in life where she sees and hears a lot of things from other children (who may have older siblings) and is in the "limbo" stage of wanting to become a tween (a bit early but I see it in my daughters friends a lot!)but still needing to be a child and do childish things.
Setting aside a day to do something just the two of you might be a start to help calm her down and get her talking about why she feels the need to act out (same with the 4 yr old but on a different level).
We all need to reconnect periodically with the ones we love and it sounds like you are her sole support while her father is overseas. Hope this helps!