I really need help with my daughter! She is 3 years old.?

I think she's becoming a bully. Anytime we are around other kids, she pushes them, she pulls and shakes on their arms really hard, and she won't stop when I give her consequences. In some cases when I ask her to stop, she does it even harder. I'm really concerned with this because she is doing it to her baby sister. Her sister will just walk by her and she will kick, push her down, smack her on the back. I don't understand why she does this because she is so sweet when she's not acting this way. I'm losing my mind because my husband works all day, so I am home with her from morning until bedtime, and I lose my cool by the end of the day. We start out having a fun day, and by bedtime I'm yelling and crying from the frustration. I really need help, and advice. Is there something wrong with my daughter?