I'm betting she is just jealous. My two year old is not usually aggressive, but gets that way when another child comes near me. When I pick him up from daycare, the other kids tend to hover around (they do this with every parent that comes into the room). My son will push them away from me. He also gets very upset if I pay attention to or pick up another child.
I'm not sure if this works with a 3 year old, but what I do is stop him immediately. I say to him "so and so is your friend and that is not how we treat our friends". "Now show mommy your gentle hands". I am very very consistent with this, but it takes time. I know every child is different and responds to different things. I find correcting the behavior at the very moment it occurs works better for us then a punishment. When he screams or yells, I tell him that mommy does not understand yelling. That he needs to calm down and tell mommy what he needs. If he keeps screaming I completely and totally ignore him. I find that no response to screaming is teaching him that he has to use his "nice" voice for mommy to pay attention or respond. Again, that is just us. Different personalities in kids require different responses.
I do home daycare and i have a 3 year old daughter, i look after 2 little boys and my daughter is very mean, rude and hits then all the time, ive tryed time outs sending her to her room nothing works she is also rude and screams at us her family, i dont know what to do