Problem With Sibling Biting, What Should We Do?

We have a serious problem with biting in our household. It started with my 1 year old son. He's not vocal yet, one way he deals with his frustration is to bit. He'll bit anyone if he's upset, especially my 4 year old daughter. They for the most part get along, unless my daughter wants to be alone. When he bothers her, she pushes, then he bites. The problem now is that my daughter is biting him back and it's turning into her biting him whenever she's frustrated. She gets him really good, leaving big welts on him arm. Have any of you experienced this and what will work to prevent this from continuing? Our pediatrician says it's just a phase. Yeah, it's a phase for my son, but my daughter shouldn't be biting anyone at all.