E., when my son was in daycare when he was a toddler (2) there was a little boy (2) there who would bite him. Maureen the daycare provider was at her wits end, she had told the parents of this little boy about this many many times and his behavior never changed. She was a day away from telling his parents that he is no longer welcome in her home for daycare.
I asked Maureen what time the parents picked up their little bitter and planned to be there at that time to voice my concern for my son and the other kids in the daycare. I arrived right before the mother did and when she walked in her son right off the bat started to be awful. He was one of those kids you see in the grocery store that you wish the parents could have left at home. He was kicking her, he even bit her in front of me. She stood there and took it all the while just telling him to be a good boy. I couldn't take it anymore. I got down to the childs level, put my hands on his shoulders and sternly told him "you do not bit, kick, or hit your mom, my son Wyatt or any other kids" He looked at him with that sad 2 year old face and started to cry. I was still at his level and asked him why he was crying, he said he was sad that I yelled at him, keep in mind I did not yell at all but I was very stern with him. I told him that the kids at daycare are sad to because he is so naughty when he is at daycare. After some crying from him, he said he was sorry, gave me a hug, gave my son a hug and I told him to go off to play with the other kids.
I looked at the mom and said that if her son did not stop the biting and all the other bad behavior that he was not allowed to come to Maureen's daycare anymore. I also told the mom that if she did not do something about her son's behavior now that when he is 6 or 7 she will have many many issues. I gave her some of the resources I have used with Wyatt, to many to list for this email. To make a long story short, her son changed his behavior, not overnight and he regressed a few times but he is now a well behaved little boy.
With regards to your situation, if this little girl continues to do what she is doing with your baby, I would say he will be in danger. She is 2 and 2 year olds are very resourcefull in getting what they want, good or bad. Her behavior is a product of her parents. They let her run their house hold and themselves. That little girl will end up being the classic little spoiled brat who then turns into the b***h in highschool.
I know you have been with them for a long time and I am sure you feel like more of a friend than an employee, but that is what you are to them in reality. You need to sit down with BOTH (if there are two) parents and lay down the ground rules on what your duties during the day, you need to discuss discipline with them and make sure you are on the same page. You can't discipline her during the day and have the parents let her run wild in the evening. Just like any other job there are expectations that come with the job and you need to have a clear job discription of what it is you do for them and how to do it. Just like a "regular" job there are things that can get you dismissed from your position, you need to make these parents understand that if this behavior continues you will have to terminate your employment with them. Your son needs to feel safe and you need to feel safe also. If you worked in an office situation and something was not right, you would take it up with your manager and voice your concerns. You need to do this with her parents. On the opposite side, if you stay and the little girl does not change her behavior, your son as he gets older will have the worst peer role model in his life. You will find that you will have the same type behavior issues with him, kids learn at an early age by watching others around them.
My step daugher is a nanny also and she had a situation similar to yours and she left that family. She is now with a new family (two sets of twins) and the expectations are very clear and it makes for a peaceful day (usually). You can love what you do but you don't have to love where you do it.
I would give the parents of the little girl a time frame for her behavior change (in writting) and if you do not see ANY improvement, you will terminate your employment.
I am sorry if I seem to be rambling, but I am tired of parents saying "what happened to my child" "why are they so bad". These parents need to look back on to themselve for part of the blame. Like the refrigerator magnet says, "children learn what they live". I hope this helps and if not for you, maybe someone else.