I believe a frank discussion is in order. She needs to know that you value her as a provider to your child, but now that the dog has bit, it is unacceptable to have your kiddo around her dog.
However... when my oldest son was 18-24 months, I lived with my mom. She had a small Shih-Tzu who did not enjoy kids. My son was continually in the dog's face and was bit and/or snapped at repeatedly. My son just wasn't getting the message to leave the dog alone. Eventually (8 or so bites later), my son finally learned that getting in the dog's face was a bad idea. While none of these bites broke the skin, one happened a day after my son had surgery on his upper lip - the dog's bite broke the scabs over the sutures and caused some bleeding (I was standing 2 feet away when it happened).
Would I sue my mom for my son's learning curve? Of course not. Is it sometimes the nature of small children to harass animals just to see what will happen? Absolutely. Can a little perspective be put on the fact that this dog is probably a valuable member of your sitter's family and that the kids probably really enjoy their playtime w/ the dog? I think so. Finally, you knew she had a dog when you chose her to care for your child. You still chose her as the best possible candidate for that most important of positions. The reasons you chose her most likely still exist. Is it worth losing one great sitter over something which could really happen anywhere, anytime, in any home on any given day across the country? Your son is fine and perhaps he learned a lesson on how to best play with the dog or how not to play. I think I'd be willing to forgive this one very normal, natural thing. But that's just me.