L.,
I can understand how you feel about someone else disciplining your child, but if your daughter was at someone else's house and she was biting other kids, would you want that to continue or would you want the parent to stop her?
I believe that an entire community is responsible for everyone's children. If I see a child playing in the street I have no problem telling them to get back on the sidewalk or go home and I make sure they follow through. If I see kids antagonizing our neighbor's dog I'll call them on it and send them home as well. I expect other parents to do the same if my child is behaving badly.
Kids learn respect not only from their parents, but also from the other adults in their lives. If they can get away with bad behavior in front of a neighbor what is to stop them from continuing that behavior in front of other adults. Over time it can escalate into dangerous and truly harmful behavior.
If you really feel uncomfortable with disciplining the other kids, talk to their parents and see how they feel. Just ask an open ended question...."If my daughter was over at your house and misbehaving, would you discipline her and how?" Then turn the tables and ask, "When your children are over at my house and are misbehaving, how would you feel if I disciplined them in the following manner?" and list how you would react to specific situations. This way you and the other parents are on the same page and everyone knows how the other adults feel.
Don't forget,you are your child's advocate until she learns how to stand up for herself. Being a mamma bear is not a bad thing. It teaches your daughter to have confidence in her parents that they will protect her from people who harm her, and also how to protect herself from those same people.
Good luck!