Children act out at home because that is where they feel safe. If a child does not feel safe at home, they will not act out. So, we know that your child feels safe while at home and that is a good thing. Now, the acting out is caused by the change in her life and the instability that not having mom around as much as caused. She needs special extra attention from her mom. Find happy things to do together, alone. Quality time with each child is a must. Reading a story is a great start. Make sure that you are communicating with her and asking her questions and talking together. It is hard to balance work, home and family. In order to be happy, the balance must be there. If you spend more time working, you will not be happy. If the mom is not happy, the children will not be happy. If the children are not happy, nobody in the house will be happy (they will make sure of that). Children demand our attention. Negative attention is better than no attention at all. Make sure she is getting positive attention, you are paying attention to her, she is getting one on one attention with you, and you are happy.
Could it be possible she is trying to get your attention sometimes negative attention is better than none, she is the middle child, maybe she still has some jealousy issues over the 15 month old, if she is the one getting punished that may make her upset and resentful. If she is at home with her Dad whilst you work does he set bounderies or is she allowed to do what she likes with him? It seems to me that the time frame this started is telling you something, make sure you are giving her plenty of positive attention and praise her when you see her doing something right, read stories play games, when you are home, she probably misses you if you wre a stay at home Mom..Good Luck